test/difference_constraints.test.cpp

test/difference_constraints.test.cpp · GitHub で見る

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#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/GRL_1_B"
#include "graph/difference_constraints.hpp"
#include "components/fast_io.hpp"

int main() {
	FastInput input;
	FastOutput output;
	int n = 0, m = 0, source = 0;
	input.read(n);
	input.read(m);
	input.read(source);
	struct Edge { int from, to; std::int64_t cost; };
	std::vector<Edge> edges(m);
	std::vector<std::vector<int>> graph(n);
	for (auto &edge : edges) {
		input.read(edge.from);
		input.read(edge.to);
		input.read(edge.cost);
		graph[edge.from].push_back(edge.to);
	}
	std::vector<bool> reachable(n);
	std::vector<int> order{source};
	reachable[source] = true;
	for (std::size_t i = 0; i < order.size(); ++i) for (int to : graph[order[i]])
		if (!reachable[to]) reachable[to] = true, order.push_back(to);
	DifferenceConstraints<> system(n);
	system.reserve(m);
	for (auto edge : edges) if (reachable[edge.from]) system.add_le(edge.from, edge.to, edge.cost);
	auto result = system.solve();
	if (!result.feasible()) {
		output.write("NEGATIVE CYCLE\n");
		return 0;
	}
	auto bounds = result.upper_bounds(source);
	for (auto bound : bounds) {
		if (bound) {
			output.write(*bound);
			output.write('\n');
		} else output.write("INF\n");
	}
}

#line 1 "test/difference_constraints.test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/GRL_1_B"
#line 1 "graph/difference_constraints.hpp"



#line 1 "graph/bellman_ford.hpp"



#line 1 "components/shortest_path_scc.hpp"



#include <algorithm>
#include <cassert>
#include <cstddef>
#include <limits>
#include <vector>

namespace negative_path_detail {
struct Components {
	std::vector<int> id, vertices;
	std::vector<std::size_t> offset{0};
};
template<class Graph>
Components reachable_components(const Graph &g, int source) {
	assert(std::size_t(g.size()) <= std::size_t(std::numeric_limits<int>::max()));
	int n = static_cast<int>(g.size());
	assert(0 <= source && source < n);
	Components result;
	result.id.assign(n, -1);
	std::vector<int> index(n, -1), low(n), pending;
	struct Frame { int vertex; std::size_t next; };
	std::vector<Frame> stack;
	int clock = 0, count = 0;
	auto enter = [&](int v) {
		index[v] = low[v] = clock++;
		pending.push_back(v);
		stack.push_back({v, 0});
	};
	enter(source);
	while (!stack.empty()) {
		int v = stack.back().vertex;
		if (stack.back().next < g[v].size()) {
			int to = g[v][stack.back().next++].first;
			assert(0 <= to && to < n);
			if (index[to] == -1) enter(to);
			else if (result.id[to] == -1) low[v] = std::min(low[v], index[to]);
		} else {
			stack.pop_back();
			if (low[v] == index[v]) {
				int u;
				do {
					u = pending.back();
					pending.pop_back();
					result.id[u] = count;
					result.vertices.push_back(u);
				} while (u != v);
				++count;
				result.offset.push_back(result.vertices.size());
			}
			if (!stack.empty()) {
				int parent = stack.back().vertex;
				low[parent] = std::min(low[parent], low[v]);
			}
		}
	}
	return result;
}
}


#line 1 "components/directed_csr.hpp"



#line 7 "components/directed_csr.hpp"
#include <cstdint>
#include <memory>
#include <span>
#include <stdexcept>
#include <type_traits>
#include <utility>
#line 14 "components/directed_csr.hpp"

namespace directed_csr_detail { struct Access; }

template<class T>
class DirectedCSR {
  public:
	struct Edge { int from, to; T weight; };
	using Arc = std::pair<int, T>;
	using weight_type = T;
	using distance_type = std::conditional_t<std::is_integral_v<T> && sizeof(T) < 8, std::int64_t, T>;

  private:
	friend struct directed_csr_detail::Access;
	std::vector<std::size_t> offset_;
	std::vector<Arc> arcs_;
	int single_gap_ = -2;
	bool unique_incoming_ = true;
	void reset(int n, std::size_t m) {
		assert(n >= 0);
		offset_.assign(std::size_t(n) + 1, 0);
		single_gap_ = -2;
		unique_incoming_ = m <= std::size_t(n);
	}
	void count_edge(const Edge &edge, std::vector<std::uint64_t> &seen) {
		assert(0 <= edge.from && edge.from < size() && 0 <= edge.to && edge.to < size());
		++offset_[edge.from];
		if (unique_incoming_) {
			auto mask = std::uint64_t(1) << (edge.to % 64);
			auto &word = seen[edge.to / 64];
			unique_incoming_ = !(word & mask);
			word |= mask;
		}
	}
	void finish(std::span<const Edge> edges) {
		const auto n = offset_.size() - 1;
		single_gap_ = -2;
		if (edges.size() >= n - (n != 0) && edges.size() <= n &&
			std::all_of(offset_.begin(), offset_.end() - 1, [](std::size_t x) { return x <= 1; })) {
			single_gap_ = -1;
			if (edges.size() != n) single_gap_ = int(std::find(offset_.begin(), offset_.end() - 1, 0) - offset_.begin());
			for (std::size_t v = 0; v <= n; ++v) offset_[v] = v - (single_gap_ >= 0 && v > std::size_t(single_gap_));
			arcs_.resize(edges.size());
			for (const auto &edge : edges) arcs_[edge.from - (single_gap_ >= 0 && edge.from > single_gap_)] = {edge.to, edge.weight};
			return;
		}
		std::size_t active = offset_[0] != 0;
		for (std::size_t v = 1; v < offset_.size(); ++v) {
			active += offset_[v] != 0;
			offset_[v] += offset_[v - 1];
		}
		arcs_.resize(edges.size());
		std::size_t i = edges.size();
#if defined(__GNUC__) || defined(__clang__)
		if (active >= 8192) {
			for (; i > 32; --i) {
				const auto from = edges[i - 33].from;
				__builtin_prefetch(&offset_[from], 1, 3);
				__builtin_prefetch(&arcs_[offset_[from] - 1], 1, 3);
				const auto &edge = edges[i - 1];
				arcs_[--offset_[edge.from]] = {edge.to, edge.weight};
			}
		}
#endif
		for (; i; --i) {
			const auto &edge = edges[i - 1];
			arcs_[--offset_[edge.from]] = {edge.to, edge.weight};
		}
	}
	void clear_edges() {
		single_gap_ = -2;
		unique_incoming_ = true;
		std::fill(offset_.begin(), offset_.end(), 0);
		arcs_.clear();
	}

  public:
	explicit DirectedCSR(int n = 0) {
		assert(n >= 0);
		offset_.assign(std::size_t(n) + 1, 0);
	}
	DirectedCSR(int n, std::span<const Edge> edges) { build(n, edges); }
	template<class Producer>
	DirectedCSR(int n, std::size_t m, Producer &&produce) { build(n, m, std::forward<Producer>(produce)); }
	void build(int n, std::span<const Edge> edges) {
		reset(n, edges.size());
		try {
			std::vector<std::uint64_t> seen(unique_incoming_ ? (std::size_t(n) + 63) / 64 : 0);
			for (const auto &edge : edges) count_edge(edge, seen);
			finish(edges);
		}
		catch (...) { clear_edges(); throw; }
	}
	template<class Producer>
	void build(int n, std::size_t m, Producer &&produce) {
		reset(n, m);
		try {
			std::vector<std::uint64_t> seen(unique_incoming_ ? (std::size_t(n) + 63) / 64 : 0);
			auto edges = std::make_unique_for_overwrite<Edge[]>(m);
			std::size_t count = 0;
			auto emit = [&](Edge edge) {
				if (count == m) throw std::length_error("DirectedCSR edge count");
				count_edge(edge, seen);
				edges[count++] = std::move(edge);
			};
			std::forward<Producer>(produce)(emit);
			if (count != m) throw std::length_error("DirectedCSR edge count");
			finish(std::span<const Edge>(edges.get(), m));
		} catch (...) { clear_edges(); throw; }
	}
	int size() const { return offset_.empty() ? 0 : int(offset_.size() - 1); }
	bool empty() const { return size() == 0; }
	std::size_t edge_count() const { return arcs_.size(); }
	std::span<const Arc> operator[](int v) const {
		assert(0 <= v && v < size());
		return std::span<const Arc>(arcs_).subspan(offset_[v], offset_[v + 1] - offset_[v]);
	}
};

namespace directed_csr_detail {
template<class T>
struct SingleEdgeView {
	std::span<const typename DirectedCSR<T>::Arc> arcs;
	int n, gap;
	int size() const { return n; }
	std::span<const typename DirectedCSR<T>::Arc> operator[](int v) const {
		if (v == gap) return {};
		return arcs.subspan(v - (gap >= 0 && v > gap), 1);
	}
};

struct Access {
	template<class T>
	static bool unique_incoming(const DirectedCSR<T> &g) { return g.offset_.empty() || g.unique_incoming_; }
	template<class T>
	static bool has_single_edge_layout(const DirectedCSR<T> &g) { return !g.offset_.empty() && g.single_gap_ >= -1; }
	template<class T>
	static SingleEdgeView<T> single_edge_view(const DirectedCSR<T> &g) { return {g.arcs_, g.size(), g.single_gap_}; }
};
}


#line 1 "components/RadixHeap.hpp"



#line 5 "components/RadixHeap.hpp"
#include <bit>
#line 13 "components/RadixHeap.hpp"

template <class Key = std::uint64_t, class T = int>
class RadixHeap {
	static_assert(std::is_integral_v<Key> && !std::is_same_v<Key, bool> && sizeof(Key) <= 8);
	using U = std::make_unsigned_t<Key>;
	using State = std::pair<Key, T>;
	std::vector<State> bucket[std::numeric_limits<U>::digits + 1];
	Key lower;
	std::size_t count = 0;
	int index(Key key) const { return std::bit_width(U(U(key) ^ U(lower))); }
	void refill() {
		assert(count);
		if (!bucket[0].empty()) return;
		int i = 1;
		while (bucket[i].empty()) ++i;
		lower = bucket[i][0].first;
		for (const auto &s : bucket[i]) lower = std::min(lower, s.first);
		for (auto &s : bucket[i]) bucket[index(s.first)].push_back(std::move(s));
		bucket[i].clear();
	}

  public:
	explicit RadixHeap(Key minimum = 0) : lower(minimum) {}
	RadixHeap(const RadixHeap &) = default;
	RadixHeap &operator=(const RadixHeap &) = default;
	RadixHeap(RadixHeap &&other) noexcept : lower(other.lower), count(std::exchange(other.count, 0)) {
		for (int i = 0; i <= std::numeric_limits<U>::digits; ++i) bucket[i] = std::move(other.bucket[i]);
	}
	RadixHeap &operator=(RadixHeap &&other) noexcept {
		if (this != &other) {
			lower = other.lower;
			count = std::exchange(other.count, 0);
			for (int i = 0; i <= std::numeric_limits<U>::digits; ++i) bucket[i] = std::move(other.bucket[i]);
		}
		return *this;
	}

	bool empty() const { return count == 0; }
	std::size_t size() const { return count; }
	Key last() const { return lower; }
	void clear(Key minimum = 0) {
		for (auto &b : bucket) b.clear();
		lower = minimum;
		count = 0;
	}
	void push(State s) {
		assert(s.first >= lower);
		bucket[index(s.first)].push_back(std::move(s));
		++count;
	}
	const State &top() {
		refill();
		return bucket[0].back();
	}
	void pop() {
		refill();
		bucket[0].pop_back();
		--count;
	}
	State pop_value() {
		refill();
		State s = std::move(bucket[0].back());
		bucket[0].pop_back();
		--count;
		return s;
	}
};


#line 8 "graph/bellman_ford.hpp"
#include <functional>
#line 12 "graph/bellman_ford.hpp"

template<class Distance>
struct BellmanFordResult {
	std::vector<Distance> distance;
	std::vector<int> parent, negative_cycle;
	std::vector<std::size_t> parent_edge, negative_cycle_edges;
	Distance infinity;
	int source;
	bool has_negative_cycle() const { return !negative_cycle.empty(); }
	bool reachable(int v) const {
		assert(!has_negative_cycle() && 0 <= v && std::size_t(v) < distance.size());
		return distance[v] != infinity;
	}
	std::vector<int> path(int v) const {
		if (!reachable(v)) return {};
		std::vector<int> result;
		for (; v != source; v = parent[v]) result.push_back(v);
		result.push_back(source);
		std::reverse(result.begin(), result.end());
		return result;
	}
	std::vector<std::size_t> path_edges(int v) const {
		if (!reachable(v)) return {};
		std::vector<std::size_t> result;
		for (; v != source; v = parent[v]) result.push_back(parent_edge[v]);
		std::reverse(result.begin(), result.end());
		return result;
	}
};

namespace negative_path_detail {
template<class Distance, class Weight>
Distance add(Distance a, Weight b) {
	static_assert(std::numeric_limits<Distance>::is_integer && std::numeric_limits<Distance>::is_signed);
	static_assert(std::numeric_limits<Weight>::is_integer && std::numeric_limits<Weight>::is_signed);
	static_assert(std::numeric_limits<Distance>::digits >= std::numeric_limits<Weight>::digits);
	Distance value;
#if defined(__GNUC__) || defined(__clang__)
	if (__builtin_add_overflow(a, Distance(b), &value)) throw std::overflow_error("Bellman-Ford distance");
#else
	Distance w = b;
	if ((w > 0 && a > std::numeric_limits<Distance>::max() - w) ||
		(w < 0 && a < std::numeric_limits<Distance>::lowest() - w)) throw std::overflow_error("Bellman-Ford distance");
	value = a + w;
#endif
	if (value == std::numeric_limits<Distance>::max()) throw std::overflow_error("Bellman-Ford infinity");
	return value;
}

template<bool Decompose, int Passes, class Distance, class Graph>
BellmanFordResult<Distance> solve(const Graph &g, int source) {
	assert(std::size_t(g.size()) <= std::size_t(std::numeric_limits<int>::max()));
	int n = static_cast<int>(g.size());
	assert(0 <= source && source < n);
	Distance inf = std::numeric_limits<Distance>::max();
	BellmanFordResult<Distance> result{std::vector<Distance>(n, inf), std::vector<int>(n, -1), {},
		std::vector<std::size_t>(n, std::size_t(-1)), {}, inf, source};
	result.distance[source] = 0;
	result.parent[source] = source;
	auto &d = result.distance;
	std::vector<int> active, order;
	auto relax = [&](int v, std::size_t i) {
		const auto &[to, w] = g[v][i];
		Distance next = add(d[v], w);
		if (next >= d[to]) return false;
		d[to] = next;
		result.parent[to] = v;
		result.parent_edge[to] = i;
		return true;
	};
	for (int pass = 0; pass < Passes; ++pass) {
		bool changed = false;
		for (int v = 0; v < n; ++v) if (d[v] != inf)
			for (std::size_t i = 0; i < g[v].size(); ++i) changed |= relax(v, i);
		if (!changed) return result;
	}
	std::vector<int> position(n, -1);
	std::vector<unsigned char> labeled(n);
	Components components;
	if constexpr (Decompose) components = reachable_components(g, source);
	else {
		components.id.assign(n, 0);
		components.vertices.resize(n);
		for (int v = 0; v < n; ++v) components.vertices[v] = v;
		components.offset.push_back(n);
	}
	struct Frame { int vertex; std::size_t next, incoming; };
	std::vector<Frame> stack;
	using State = std::pair<Distance, int>;
	constexpr bool radix = std::is_integral_v<Distance> && sizeof(Distance) <= 8;
	std::conditional_t<radix, RadixHeap<Distance>, std::vector<State>> heap;
	for (int c = static_cast<int>(components.offset.size()) - 2; c >= 0; --c) {
		auto begin = components.offset[c], end = components.offset[c + 1];
		auto internal = [&](int to) { return components.id[to] == c; };
		bool negative = !Decompose;
		Distance minimum = inf;
		for (auto j = begin; j < end; ++j) {
			int v = components.vertices[j];
			minimum = std::min(minimum, d[v]);
			if constexpr (Decompose)
				for (const auto &[to, w] : g[v]) if (internal(to) && w < 0) negative = true;
		}
		if (minimum == inf) continue;
		if (negative) {
			active.clear();
			for (auto j = begin; j < end; ++j) {
				int v = components.vertices[j];
				if (d[v] != inf) active.push_back(v);
			}
			while (!active.empty()) {
				order.clear();
				for (int v : active) labeled[v] = 0;
				for (int root : active) {
					if (position[root] != -1) continue;
					bool useful = false;
					for (const auto &[to, w] : g[root])
						if (internal(to) && add(d[root], w) < d[to]) { useful = true; break; }
					if (!useful) continue;
					position[root] = 0;
					stack.push_back({root, 0, std::size_t(-1)});
					while (!stack.empty()) {
						int v = stack.back().vertex;
						if (stack.back().next == g[v].size()) {
							position[v] = -2;
							order.push_back(v);
							stack.pop_back();
							continue;
						}
						std::size_t i = stack.back().next++;
						int to = g[v][i].first;
						if (!internal(to) || !relax(v, i)) continue;
						if (position[to] >= 0) {
							for (auto j = std::size_t(position[to]); j < stack.size(); ++j) {
								result.negative_cycle.push_back(stack[j].vertex);
								if (j + 1 < stack.size()) result.negative_cycle_edges.push_back(stack[j + 1].incoming);
							}
							result.negative_cycle.push_back(to);
							result.negative_cycle_edges.push_back(i);
							return result;
						}
						if (position[to] == -1) {
							position[to] = static_cast<int>(stack.size());
							stack.push_back({to, 0, i});
						}
					}
				}
				active.clear();
				for (auto it = order.rbegin(); it != order.rend(); ++it) {
					int v = *it;
					for (std::size_t i = 0; i < g[v].size(); ++i) {
						int to = g[v][i].first;
						if (internal(to) && relax(v, i) && !labeled[to]) active.push_back(to), labeled[to] = 1;
					}
				}
				for (int v : order) position[v] = -1;
			}
		} else if (end - begin > 1) {
			auto push = [&](Distance cost, int v) {
				if constexpr (radix) heap.push({cost, v});
				else { heap.emplace_back(cost, v); std::push_heap(heap.begin(), heap.end(), std::greater<State>()); }
			};
			if constexpr (radix) heap.clear(minimum);
			for (auto j = begin; j < end; ++j) {
				int v = components.vertices[j];
				if (d[v] != inf) push(d[v], v);
			}
			while (!heap.empty()) {
				auto [cost, v] = [&] {
					if constexpr (radix) return heap.pop_value();
					else { std::pop_heap(heap.begin(), heap.end(), std::greater<State>()); auto state = heap.back(); heap.pop_back(); return state; }
				}();
				if (cost != d[v]) continue;
				for (std::size_t i = 0; i < g[v].size(); ++i) {
					int to = g[v][i].first;
					if (internal(to) && relax(v, i)) push(d[to], to);
				}
			}
		}
		if constexpr (Decompose)
			for (auto j = begin; j < end; ++j) {
				int v = components.vertices[j];
				for (std::size_t i = 0; i < g[v].size(); ++i) if (!internal(g[v][i].first)) relax(v, i);
			}
	}
	return result;
}
}

template<class Distance = std::int64_t, class Graph>
BellmanFordResult<Distance> bellman_ford(const Graph &g, int source) {
	return negative_path_detail::solve<true, 2, Distance>(g, source);
}

template<class Distance = std::int64_t, class Graph>
BellmanFordResult<Distance> goldberg_radzik(const Graph &g, int source) {
	return negative_path_detail::solve<false, 0, Distance>(g, source);
}


#line 1 "graph/dijkstra.hpp"



#line 1 "components/dijkstra_queue.hpp"



#line 15 "components/dijkstra_queue.hpp"

namespace shortest_path_detail {
template<class Weight, class Distance>
bool reaches_limit(const Weight &weight, const Distance &limit) {
	if constexpr (std::numeric_limits<Weight>::is_integer && std::numeric_limits<Weight>::is_bounded &&
				  std::numeric_limits<Distance>::is_integer && std::numeric_limits<Distance>::is_bounded) {
		using Compare = std::common_type_t<Weight, Distance>;
		return Compare(weight) >= Compare(limit);
	} else return weight >= limit;
}

template<class T> class RadixQueue {
	static_assert(std::is_integral_v<T> && sizeof(T) <= 8);
	struct State { T key; int vertex; };
	State small_[32];
	std::vector<std::uint64_t> buckets_[33];
	std::uint32_t minimum_[33];
	std::uint32_t occupied_ = 0;
	std::uint64_t last_ = 0;
	std::size_t count_ = 0;
	int mode_ = 0;
	RadixHeap<std::uint64_t> wide_;
	void put(std::uint64_t state) {
		std::uint32_t key = state >> 32;
		int index = std::bit_width(key ^ std::uint32_t(last_));
		buckets_[index].push_back(state);
		if (index) {
			occupied_ |= std::uint32_t(1) << (index - 1);
			minimum_[index] = std::min(minimum_[index], key);
		}
	}
	void promote() {
		if (mode_ == 0) {
			for (std::size_t i = 0; i < count_; ++i) wide_.push({std::uint64_t(small_[i].key), small_[i].vertex});
		} else {
			for (auto &bucket : buckets_) {
				for (auto state : bucket) {
					std::uint64_t key = last_ + std::uint32_t(std::uint32_t(state >> 32) - std::uint32_t(last_));
					wide_.push({key, int(std::uint32_t(state))});
				}
				bucket.clear();
			}
		}
		mode_ = 2;
	}

  public:
	bool empty() const { return count_ == 0; }
	void push(T key, int vertex) {
		assert(key >= 0 && std::uint64_t(key) >= last_);
		if (mode_ == 0 && count_ < 32) {
			small_[count_++] = {key, vertex};
			return;
		}
		if (mode_ == 0) {
			bool narrow = std::uint64_t(key) - last_ <= std::uint64_t(std::numeric_limits<std::int32_t>::max());
			for (std::size_t i = 0; i < count_; ++i)
				narrow &= std::uint64_t(small_[i].key) - last_ <= std::uint64_t(std::numeric_limits<std::int32_t>::max());
			if (narrow) {
				std::fill_n(minimum_, 33, std::numeric_limits<std::uint32_t>::max());
				for (std::size_t i = 0; i < count_; ++i)
					put((std::uint64_t(std::uint32_t(small_[i].key)) << 32) | std::uint32_t(small_[i].vertex));
				mode_ = 1;
			} else promote();
		}
		if (mode_ == 1 && std::uint64_t(key) - last_ > std::uint64_t(std::numeric_limits<std::int32_t>::max())) promote();
		if (mode_ == 2) wide_.push({std::uint64_t(key), vertex});
		else put((std::uint64_t(std::uint32_t(key)) << 32) | std::uint32_t(vertex));
		++count_;
	}
	std::pair<T, int> pop() {
		assert(count_);
		if (mode_ == 0) {
			std::size_t best = 0;
			for (std::size_t i = 1; i < count_; ++i)
				if (small_[i].key < small_[best].key) best = i;
			State state = small_[best];
			small_[best] = small_[--count_];
			last_ = std::uint64_t(state.key);
			return {state.key, state.vertex};
		}
		if (mode_ == 2) {
			auto state = wide_.pop_value();
			last_ = state.first;
			--count_;
			return {T(state.first), state.second};
		}
		if (buckets_[0].empty()) {
			int index = std::countr_zero(occupied_) + 1;
			last_ += std::uint32_t(minimum_[index] - std::uint32_t(last_));
			minimum_[index] = std::numeric_limits<std::uint32_t>::max();
			occupied_ &= occupied_ - 1;
			if (buckets_[index].size() == 1) {
				auto state = buckets_[index].back();
				buckets_[index].clear();
				--count_;
				return {T(last_), int(std::uint32_t(state))};
			}
			for (auto state : buckets_[index]) put(state);
			buckets_[index].clear();
		}
		auto state = buckets_[0].back();
		buckets_[0].pop_back();
		--count_;
		return {T(last_), int(std::uint32_t(state))};
	}
};

template<class T> class BinaryQueue {
	using State = std::pair<T, int>;
	std::vector<State> heap_;

  public:
	bool empty() const { return heap_.empty(); }
	void push(T cost, int vertex) {
		heap_.emplace_back(std::move(cost), vertex);
		std::push_heap(heap_.begin(), heap_.end(), std::greater<State>());
	}
	State pop() {
		std::pop_heap(heap_.begin(), heap_.end(), std::greater<State>());
		State state = std::move(heap_.back());
		heap_.pop_back();
		return state;
	}
};

template<class T>
using DistanceQueue = std::conditional_t<std::is_integral_v<T> && sizeof(T) <= 8, RadixQueue<T>, BinaryQueue<T>>;
}


#line 1 "components/dijkstra_topological.hpp"



#line 11 "components/dijkstra_topological.hpp"

namespace shortest_path_detail {
template<bool Path, class G, class T>
std::vector<T> topological_run(const G &g, int start, int target, T inf, std::vector<int> &parent) {
	std::size_t n = std::size_t(g.size());
	assert(n <= static_cast<std::size_t>(std::numeric_limits<int>::max()));
	assert(start >= 0 && static_cast<std::size_t>(start) < n);
	assert(inf > 0);
	std::vector<T> distance(n, inf);
	std::vector<std::size_t> indegree(n);
	std::vector<int> ready;
	ready.reserve(n);
	for (std::size_t v = 0; v < n; ++v)
		for (const auto &[to, weight] : g[int(v)]) {
			assert(to >= 0 && static_cast<std::size_t>(to) < n);
			assert(weight >= 0);
			++indegree[to];
		}
	for (std::size_t v = 0; v < n; ++v)
		if (!indegree[v]) ready.push_back(int(v));
	distance[start] = 0;
	auto improve = [&](int from, const T &cost, const T &allowance, int to, const auto &weight) {
		if (reaches_limit(weight, allowance)) return false;
		T next = cost + weight;
		if (next >= distance[to]) return false;
		if constexpr (Path) {
			if (next >= distance[target]) return false;
			parent[to] = from;
		}
		distance[to] = std::move(next);
		return true;
	};
	for (std::size_t head = 0; head < ready.size(); ++head) {
		int v = ready[head];
		if constexpr (Path) if (v == target) return distance;
		T cost = distance[v];
		bool active = cost < inf;
		if constexpr (Path) active &= cost < distance[target];
		T allowance = active ? inf - cost : T(0);
		for (const auto &[to, weight] : g[v]) {
			if (active) improve(v, cost, allowance, to, weight);
			if (--indegree[to] == 0) ready.push_back(to);
		}
	}
	DistanceQueue<T> queue;
	for (std::size_t v = 0; v < n; ++v) {
		if (!indegree[v] || distance[v] == inf || g[v].empty()) continue;
		if constexpr (Path) if (int(v) == target || distance[v] >= distance[target]) continue;
		queue.push(distance[v], int(v));
	}
	while (!queue.empty()) {
		const auto [cost, v] = queue.pop();
		if (cost != distance[v]) continue;
		if constexpr (Path) if (cost >= distance[target]) break;
		T allowance = inf - cost;
		for (const auto &[to, weight] : g[v]) {
			if (!improve(v, cost, allowance, to, weight)) continue;
			if constexpr (Path) if (to == target) continue;
			if (!g[to].empty()) queue.push(distance[to], to);
		}
	}
	return distance;
}
}


#line 1 "components/dijkstra_unique.hpp"



#line 9 "components/dijkstra_unique.hpp"

namespace shortest_path_detail {
template<class G, class T>
std::pair<T, std::vector<int>> unique_path(const G &g, int st, int target, T inf, std::vector<int> &parent) {
	using State = std::pair<T, int>;
	std::vector<State> pending;
	pending.emplace_back(T(0), st);
	while (!pending.empty()) {
		auto [cost, v] = std::move(pending.back());
		pending.pop_back();
		for (const auto &first : g[v]) {
			const auto *edge = &first;
			int from = v;
			T prefix = cost;
			for (;;) {
				const auto &[to, weight] = *edge;
				assert(weight >= 0);
				if (to == st) break;
				if (reaches_limit(weight, T(inf - prefix))) break;
				T next = prefix + weight;
				if (to == target) {
					std::vector<int> path{to};
					for (int u = from; u != st; u = parent[u]) path.push_back(u);
					path.push_back(st);
					std::reverse(path.begin(), path.end());
					return {std::move(next), std::move(path)};
				}
				const auto &outgoing = g[to];
				if (outgoing.empty()) break;
				parent[to] = from;
				if (outgoing.size() != 1) {
					pending.emplace_back(std::move(next), to);
					break;
				}
				from = to;
				edge = &outgoing[0];
				prefix = std::move(next);
			}
		}
	}
	return {T(-1), {}};
}
}


#line 16 "graph/dijkstra.hpp"

inline constexpr std::int64_t DIJKSTRA_INF = 4'000'000'000'000'000'000;

namespace shortest_path_detail {
template<class T> T infinity() {
	if constexpr (std::numeric_limits<T>::is_bounded && std::numeric_limits<T>::is_integer && std::numeric_limits<T>::digits < 62)
		return std::numeric_limits<T>::max();
	else return T(DIJKSTRA_INF);
}

template<bool Path, class G, class T>
std::vector<T> run(const G &g, int st, int target, T inf, std::vector<int> &parent) {
	const auto n = static_cast<std::size_t>(g.size());
	assert(n <= static_cast<std::size_t>(std::numeric_limits<int>::max()));
	assert(st >= 0 && static_cast<std::size_t>(st) < n);
	assert(inf > 0);
	std::vector<T> d(n, inf);
	d[st] = 0;
	DistanceQueue<T> pq;
	pq.push(0, st);
	while (!pq.empty()) {
		const auto [cost, v] = pq.pop();
		if (d[v] != cost) continue;
		if constexpr (Path) if (cost >= d[target]) break;
		T allowance = inf - cost;
		for (const auto &[to, c] : g[v]) {
			assert(to >= 0 && static_cast<std::size_t>(to) < n);
			assert(c >= 0);
			if (reaches_limit(c, allowance)) continue;
			T next = cost + c;
			if (next >= d[to]) continue;
			if constexpr (Path) {
				if (next >= d[target]) continue;
				parent[to] = v;
			}
			d[to] = next;
			if constexpr (Path) if (to == target) continue;
			if (!g[to].empty()) pq.push(std::move(next), to);
		}
	}
	return d;
}

template<bool Topological, class G, class T>
std::vector<T> distances(const G &g, int st, T inf) {
	std::vector<int> parent;
	auto d = [&] {
		if constexpr (Topological) return topological_run<false>(g, st, -1, inf, parent);
		else return run<false>(g, st, -1, inf, parent);
	}();
	for (T &val : d)
		if (val == inf) val = -1;
	return d;
}

template<bool Topological, class G, class T>
std::pair<T, std::vector<int>> path(const G &g, int st, int target, T inf) {
	[[maybe_unused]] const auto n = static_cast<std::size_t>(g.size());
	assert(n <= static_cast<std::size_t>(std::numeric_limits<int>::max()));
	assert(st >= 0 && static_cast<std::size_t>(st) < n);
	assert(target >= 0 && static_cast<std::size_t>(target) < n);
	assert(inf > 0);
	if (st == target) return {T(0), {st}};
	if (g[st].empty()) return {T(-1), {}};
	if (g[st].size() == 1) {
		using Weight = std::remove_cvref_t<decltype(g[st][0].second)>;
		std::vector<int> direct{st};
		T cost = 0;
		int v = st, checkpoint = st;
		std::size_t power = 1, length = 0;
		while (g[v].size() == 1) {
			const auto &[to, weight] = g[v][0];
			assert(to >= 0 && static_cast<std::size_t>(to) < n);
			assert(weight >= 0);
			if (reaches_limit(weight, T(inf - cost))) return {T(-1), {}};
			cost += weight;
			v = to;
			direct.push_back(v);
			if (v == target) return {std::move(cost), std::move(direct)};
			if (v == checkpoint) return {T(-1), {}};
			if (++length == power) {
				checkpoint = v;
				power *= 2;
				length = 0;
			}
		}
		if (g[v].empty()) return {T(-1), {}};
		if constexpr (std::numeric_limits<Weight>::is_integer && std::numeric_limits<T>::is_integer && std::numeric_limits<T>::is_bounded) {
			auto suffix = shortest_path_detail::path<Topological>(g, v, target, T(inf - cost));
			if (suffix.first == T(-1)) return {T(-1), {}};
			direct.pop_back();
			direct.insert(direct.end(), suffix.second.begin(), suffix.second.end());
			return {cost + suffix.first, std::move(direct)};
		}
	}
	std::vector<int> parent(g.size(), -1);
	if constexpr (requires { directed_csr_detail::Access::unique_incoming(g); })
		if (directed_csr_detail::Access::unique_incoming(g)) return unique_path(g, st, target, inf, parent);
	auto d = [&] {
		if constexpr (Topological) return topological_run<true>(g, st, target, inf, parent);
		else return run<true>(g, st, target, inf, parent);
	}();
	if (d[target] == inf) return {T(-1), {}};
	std::vector<int> path;
	for (int v = target; v != st; v = parent[v]) path.push_back(v);
	path.push_back(st);
	std::reverse(path.begin(), path.end());
	return {std::move(d[target]), std::move(path)};
}
}

template<bool Topological, class T>
std::vector<T> dijkstra(const std::vector<std::vector<std::pair<int, T>>> &g, int st, T inf = shortest_path_detail::infinity<T>()) {
	return shortest_path_detail::distances<Topological>(g, st, inf);
}

template<class T>
std::vector<T> dijkstra(const std::vector<std::vector<std::pair<int, T>>> &g, int st, T inf = shortest_path_detail::infinity<T>()) {
	return dijkstra<false>(g, st, inf);
}

template<bool Topological, class T>
std::pair<T, std::vector<int>> dijkstra_path(const std::vector<std::vector<std::pair<int, T>>> &g, int st, int target, T inf = shortest_path_detail::infinity<T>()) {
	return shortest_path_detail::path<Topological>(g, st, target, inf);
}

template<class T>
std::pair<T, std::vector<int>> dijkstra_path(const std::vector<std::vector<std::pair<int, T>>> &g, int st, int target, T inf = shortest_path_detail::infinity<T>()) {
	return dijkstra_path<false>(g, st, target, inf);
}

template<bool Topological, class W, class T = typename DirectedCSR<W>::distance_type>
std::vector<T> dijkstra(const DirectedCSR<W> &g, int st, T inf = shortest_path_detail::infinity<T>()) {
	return shortest_path_detail::distances<Topological>(g, st, inf);
}

template<class W, class T = typename DirectedCSR<W>::distance_type>
std::vector<T> dijkstra(const DirectedCSR<W> &g, int st, T inf = shortest_path_detail::infinity<T>()) {
	return dijkstra<false>(g, st, inf);
}

template<bool Topological, class W, class T = typename DirectedCSR<W>::distance_type>
std::pair<T, std::vector<int>> dijkstra_path(const DirectedCSR<W> &g, int st, int target, T inf = shortest_path_detail::infinity<T>()) {
	if (directed_csr_detail::Access::has_single_edge_layout(g))
		return shortest_path_detail::path<Topological>(directed_csr_detail::Access::single_edge_view(g), st, target, inf);
	return shortest_path_detail::path<Topological>(g, st, target, inf);
}

template<class W, class T = typename DirectedCSR<W>::distance_type>
std::pair<T, std::vector<int>> dijkstra_path(const DirectedCSR<W> &g, int st, int target, T inf = shortest_path_detail::infinity<T>()) {
	return dijkstra_path<false>(g, st, target, inf);
}


#line 6 "graph/difference_constraints.hpp"
#include <optional>

template<class Cost = std::int64_t>
class DifferenceConstraints {
	static_assert(std::numeric_limits<Cost>::is_integer && std::numeric_limits<Cost>::is_signed && sizeof(Cost) <= 16);

  public:
	using value_type = std::conditional_t<(sizeof(Cost) <= 8), std::int64_t, __int128_t>;
	using Constraint = DirectedCSR<value_type>::Edge;
	class Result {
		friend class DifferenceConstraints;
		int n_;
		DirectedCSR<value_type> graph_;
		std::vector<value_type> values_;
		std::vector<Constraint> negative_cycle_;
		explicit Result(int n) : n_(n) {}
		void check([[maybe_unused]] int v) const { assert(0 <= v && v <= n_); }
		value_type potential(int v) const { return v == n_ ? 0 : values_[v]; }
		template<class Function>
		auto with_distances(int source, Function &&function) const {
			assert(feasible());
			check(source);
			if (!n_) return function(std::vector<value_type>{0});
			auto distance = dijkstra(graph_, source, std::numeric_limits<value_type>::max());
			if (std::find(distance.begin(), distance.end(), value_type(-1)) != distance.end())
				for (int v = 0; v <= n_; ++v) if (distance[v] != -1)
					for (auto [to, weight] : graph_[v])
						if (distance[to] == -1) throw std::overflow_error("DifferenceConstraints distance");
			return function(distance);
		}

	  public:
		Result(const Result &) = default;
		Result &operator=(const Result &) = default;
		Result(Result &&other) noexcept : n_(std::exchange(other.n_, 0)), graph_(std::move(other.graph_)),
			values_(std::move(other.values_)), negative_cycle_(std::move(other.negative_cycle_)) {}
		Result &operator=(Result &&other) noexcept {
			if (this != &other) {
				n_ = std::exchange(other.n_, 0);
				graph_ = std::move(other.graph_);
				values_ = std::move(other.values_);
				negative_cycle_ = std::move(other.negative_cycle_);
			}
			return *this;
		}
		int size() const { return n_; }
		int origin() const { return n_; }
		bool feasible() const { return negative_cycle_.empty(); }
		const std::vector<value_type> &values() const { assert(feasible()); return values_; }
		value_type value(int v) const { assert(feasible()); check(v); return potential(v); }
		const std::vector<Constraint> &negative_cycle() const { return negative_cycle_; }
		std::vector<std::optional<value_type>> upper_bounds(int source) const {
			return with_distances(source, [&](const auto &reduced) {
				std::vector<std::optional<value_type>> result(n_);
				for (int v = 0; v < n_; ++v)
					if (reduced[v] != -1) result[v] = add_sub(reduced[v], potential(v), potential(source));
				return result;
			});
		}
		std::vector<std::optional<value_type>> upper_bounds() const { return upper_bounds(origin()); }
		std::optional<value_type> max_difference(int u, int v) const {
			assert(feasible());
			check(u), check(v);
			if (u == v) return 0;
			return with_distances(u, [&](const auto &reduced) -> std::optional<value_type> {
				if (reduced[v] == -1) return std::nullopt;
				return add_sub(reduced[v], potential(v), potential(u));
			});
		}
		std::optional<value_type> min_difference(int u, int v) const {
			auto result = max_difference(v, u);
			if (result) *result = checked_sub(0, *result);
			return result;
		}
		std::optional<value_type> upper_bound(int v) const { return max_difference(origin(), v); }
		std::optional<value_type> lower_bound(int v) const { return min_difference(origin(), v); }
	};

  private:
	int n_;
	std::vector<Constraint> constraints_;
	void check([[maybe_unused]] int v) const { assert(0 <= v && v <= n_); }
	std::size_t add(int u, int v, value_type bound) {
		check(u), check(v);
		constraints_.push_back({u, v, bound});
		return constraints_.size() - 1;
	}
	static value_type checked_add(value_type a, value_type b) {
		value_type result;
		if (__builtin_add_overflow(a, b, &result)) throw std::overflow_error("DifferenceConstraints addition");
		return result;
	}
	static value_type checked_sub(value_type a, value_type b) {
		value_type result;
		if (__builtin_sub_overflow(a, b, &result)) throw std::overflow_error("DifferenceConstraints subtraction");
		return result;
	}
	static value_type add_sub(value_type a, value_type b, value_type c) {
		if ((b < 0) == (c < 0)) return checked_add(a, checked_sub(b, c));
		return checked_sub(checked_add(a, b), c);
	}

  public:
	explicit DifferenceConstraints(int n = 0) : n_(n) { assert(0 <= n && n <= std::numeric_limits<int>::max() - 2); }
	int size() const { return n_; }
	int origin() const { return n_; }
	std::size_t constraint_count() const { return constraints_.size(); }
	const std::vector<Constraint> &constraints() const { return constraints_; }
	void reserve(std::size_t count) { constraints_.reserve(count); }
	std::size_t add_le(int u, int v, Cost bound) { return add(u, v, value_type(bound)); }
	std::size_t add_ge(int u, int v, Cost bound) { return add(v, u, checked_sub(0, value_type(bound))); }
	std::size_t add_lt(int u, int v, Cost bound) { return add(u, v, checked_sub(value_type(bound), 1)); }
	std::size_t add_gt(int u, int v, Cost bound) { return add(v, u, checked_sub(-1, value_type(bound))); }
	std::pair<std::size_t, std::size_t> add_eq(int u, int v, Cost value) {
		value_type reverse = checked_sub(0, value_type(value));
		return {add(u, v, value), add(v, u, reverse)};
	}
	std::pair<std::size_t, std::size_t> add_range(int u, int v, Cost lower, Cost upper) {
		value_type reverse = checked_sub(0, value_type(lower));
		return {add(v, u, reverse), add(u, v, upper)};
	}
	std::size_t add_upper_bound(int v, Cost bound) { return add_le(origin(), v, bound); }
	std::size_t add_lower_bound(int v, Cost bound) { return add_ge(origin(), v, bound); }
	std::pair<std::size_t, std::size_t> fix(int v, Cost value) { return add_eq(origin(), v, value); }
	std::pair<std::size_t, std::size_t> add_range(int v, Cost lower, Cost upper) { return add_range(origin(), v, lower, upper); }
	Result solve() const {
		Result result(n_);
		std::vector<Constraint> edges = constraints_;
		edges.reserve(constraints_.size() + std::size_t(n_) + 1);
		const int source = n_ + 1;
		for (int v = 0; v <= n_; ++v) edges.push_back({source, v, 0});
		{
			DirectedCSR<value_type> graph(n_ + 2, edges);
			auto found = bellman_ford<value_type>(graph, source);
			if (found.has_negative_cycle()) {
				for (std::size_t i = 0; i < found.negative_cycle_edges.size(); ++i) {
					int from = found.negative_cycle[i];
					auto [to, weight] = graph[from][found.negative_cycle_edges[i]];
					assert(from <= n_ && to <= n_);
					result.negative_cycle_.push_back({from, to, weight});
				}
				return result;
			}
			result.values_.resize(n_);
			for (int v = 0; v < n_; ++v) result.values_[v] = checked_sub(found.distance[v], found.distance[n_]);
		}
		edges.resize(constraints_.size());
		for (auto &edge : edges) {
			edge.weight = add_sub(edge.weight, result.potential(edge.from), result.potential(edge.to));
			assert(edge.weight >= 0);
			if (edge.weight == std::numeric_limits<value_type>::max()) throw std::overflow_error("DifferenceConstraints reduced weight");
		}
		result.graph_ = DirectedCSR<value_type>(n_ + 1, edges);
		return result;
	}
};


#line 1 "components/fast_io.hpp"



#line 5 "components/fast_io.hpp"
#include <array>
#line 8 "components/fast_io.hpp"
#include <charconv>
#line 11 "components/fast_io.hpp"
#include <cstdio>
#include <cstring>
#line 15 "components/fast_io.hpp"
#include <string>
#include <string_view>
#line 18 "components/fast_io.hpp"
#if defined(__unix__) || defined(__APPLE__)
#include <sys/mman.h>
#include <sys/stat.h>
#include <unistd.h>
#endif

namespace fast_io_detail { struct BulkInput; struct BulkOutput; }

class FastInput {
	friend struct fast_io_detail::BulkInput;
	static constexpr std::size_t capacity = 1 << 16;
	FILE *file = nullptr;
	std::unique_ptr<char[]> buffer;
	const char *current = "", *end = current;
	std::string scratch;
	void *mapping = nullptr;
	std::size_t mapped_size = 0;
	bool refill() {
		if (!file) return false;
		std::size_t n = std::fread(buffer.get(), 1, capacity, file);
		current = buffer.get();
		end = current + n;
		return n;
	}
	static const char *scan(const char *p, const char *end) {
		while (end - p >= 8) {
			std::uint64_t x;
			std::memcpy(&x, p, 8);
			if ((x - 0x2121212121212121ULL) & ~x & 0x8080808080808080ULL) break;
			p += 8;
		}
		while (p != end && static_cast<unsigned char>(*p) > ' ') ++p;
		return p;
	}

public:
	explicit FastInput(FILE *input = stdin) {
#if defined(__unix__) || defined(__APPLE__)
		struct stat status;
		int fd = fileno(input);
		auto offset = ftello(input);
		if (fd >= 0 && offset >= 0 && !fstat(fd, &status) && S_ISREG(status.st_mode) && status.st_size > offset) {
			mapped_size = status.st_size;
			mapping = mmap(nullptr, mapped_size, PROT_READ, MAP_PRIVATE, fd, 0);
			if (mapping != MAP_FAILED) {
				current = static_cast<const char *>(mapping) + offset;
				end = static_cast<const char *>(mapping) + mapped_size;
				return;
			}
			mapping = nullptr;
		}
#endif
		file = input;
		buffer = std::make_unique_for_overwrite<char[]>(capacity);
	}
	explicit FastInput(std::string_view input) : current(input.empty() ? "" : input.data()), end(current + input.size()) {}
	FastInput(const FastInput &) = delete;
	FastInput &operator=(const FastInput &) = delete;
	~FastInput() {
#if defined(__unix__) || defined(__APPLE__)
		if (mapping) munmap(mapping, mapped_size);
#endif
	}
	std::string_view token() {
		while (true) {
			while (current != end && static_cast<unsigned char>(*current) <= ' ') ++current;
			if (current != end) break;
			if (!refill()) return {};
		}
		const char *begin = current;
		current = scan(current, end);
		if (current != end || !file) return {begin, std::size_t(current - begin)};
		scratch.assign(begin, end);
		while (refill()) {
			current = scan(current, end);
			scratch.append(buffer.get(), std::size_t(current - buffer.get()));
			if (current != end) break;
		}
		return scratch;
	}
	template <class T>
	bool read(T &value) {
		if constexpr (std::is_integral_v<T> && !std::is_same_v<T, bool>) {
			while (true) {
				while (current != end && static_cast<unsigned char>(*current) <= ' ') ++current;
				if (current != end) break;
				if (!refill()) return false;
			}
			if constexpr (std::is_unsigned_v<T> && sizeof(T) == 4 && std::endian::native == std::endian::little) {
				if (end - current >= 11) {
					std::uint64_t x;
					std::memcpy(&x, current, 8);
					if (!(((x + 0x4646464646464646ULL) | (x - 0x3030303030303030ULL)) & 0x8080808080808080ULL)) {
						x &= 0x0f0f0f0f0f0f0f0fULL;
						x = (x * 10 + (x >> 8)) & 0x00ff00ff00ff00ffULL;
						x = (x * 100 + (x >> 16)) & 0x0000ffff0000ffffULL;
						std::uint64_t v = std::uint32_t(x * 10000 + (x >> 32));
						int n = 8;
						for (; n < 10 && static_cast<unsigned char>(current[n]) - unsigned('0') < 10; ++n)
							v = v * 10 + (current[n] - '0');
						if (static_cast<unsigned char>(current[n]) <= ' ' && v <= 0xffffffffULL) {
							current += n;
							value = T(v);
							return true;
						}
					}
				}
			}
			T parsed{};
			auto result = std::from_chars(current, end, parsed);
			if (result.ec == std::errc{} && (result.ptr != end ? static_cast<unsigned char>(*result.ptr) <= ' ' : !file)) {
				current = result.ptr;
				value = parsed;
				return true;
			}
		}
		auto s = token();
		if (s.empty()) return false;
		if constexpr (std::is_same_v<T, bool>) {
			assert(s == "0" || s == "1");
			value = s[0] == '1';
		} else if constexpr (std::is_integral_v<T>) {
			auto result = std::from_chars(s.data(), s.data() + s.size(), value);
			assert(result.ec == std::errc{} && result.ptr == s.data() + s.size());
			(void)result;
		} else value = T(s);
		return true;
	}
};

class FastOutput {
	friend struct fast_io_detail::BulkOutput;
	inline static constexpr auto quads = [] {
		std::array<std::array<char, 4>, 10000> table{};
		for (int i = 0; i < 10000; ++i)
			table[i] = {char('0' + i / 1000), char('0' + i / 100 % 10), char('0' + i / 10 % 10), char('0' + i % 10)};
		return table;
	}();
	FILE *file;
	std::unique_ptr<char[]> buffer = std::make_unique_for_overwrite<char[]>(1 << 16);
	std::size_t capacity = 1 << 16, length = 0;
	char *reserve(std::size_t n) {
		if (n > capacity - length) {
			if (!flush()) throw std::runtime_error("output failed");
			if (n > capacity) {
				std::size_t next = std::max(n, 2 * capacity);
				buffer = std::make_unique_for_overwrite<char[]>(next);
				capacity = next;
			}
		}
		return buffer.get() + length;
	}

public:
	explicit FastOutput(FILE *output = stdout) : file(output) {}
	FastOutput(const FastOutput &) = delete;
	FastOutput &operator=(const FastOutput &) = delete;
	~FastOutput() { flush(); }
	bool flush() {
		std::size_t offset = 0;
		while (offset < length) {
			auto n = std::fwrite(buffer.get() + offset, 1, length - offset, file);
			if (!n) {
				std::memmove(buffer.get(), buffer.get() + offset, length - offset);
				length -= offset;
				return false;
			}
			offset += n;
		}
		length = 0;
		return std::fflush(file) == 0;
	}
	void write(char c) { *reserve(1) = c; ++length; }
	void write(__uint128_t value) {
		char digits[40];
		char *end = digits + sizeof(digits), *begin = end;
		do { *--begin = char('0' + value % 10); value /= 10; } while (value);
		write(std::string_view(begin, end - begin));
	}
	void write(__int128_t value) {
		__uint128_t magnitude = __uint128_t(value);
		if (value < 0) write('-'), magnitude = 0 - magnitude;
		write(magnitude);
	}
	void write(std::string_view s) {
		char *out = reserve(s.size());
		if (!s.empty()) std::memcpy(out, s.data(), s.size());
		length += s.size();
	}
	template <class T> requires std::is_integral_v<T>
	void write(T value) {
		char *out = reserve(32);
		if constexpr (std::is_same_v<T, bool>) *out = '0' + value, ++length;
		else if constexpr (std::is_unsigned_v<T> && sizeof(T) == 4) {
			char *p = out;
			if (value >= 100000000) {
				auto high = value / 100000000, low = value % 100000000;
				p = std::to_chars(p, p + 2, high).ptr;
				std::memcpy(p, quads[low / 10000].data(), 4);
				std::memcpy(p + 4, quads[low % 10000].data(), 4);
				p += 8;
			} else if (value >= 10000) {
				p = std::to_chars(p, p + 4, value / 10000).ptr;
				std::memcpy(p, quads[value % 10000].data(), 4);
				p += 4;
			} else p = std::to_chars(p, p + 4, value).ptr;
			length += p - out;
		} else length += std::to_chars(out, out + 32, value).ptr - out;
	}
	template <class T> requires requires(const T &value, char *out) { value.decimal_capacity(); value.to_chars(out); }
	void write(const T &value) {
		char *out = reserve(value.decimal_capacity());
		length += value.to_chars(out) - out;
	}
	template <class T>
	void println(const T &value) { write(value); write('\n'); }
};


#line 4 "test/difference_constraints.test.cpp"

int main() {
	FastInput input;
	FastOutput output;
	int n = 0, m = 0, source = 0;
	input.read(n);
	input.read(m);
	input.read(source);
	struct Edge { int from, to; std::int64_t cost; };
	std::vector<Edge> edges(m);
	std::vector<std::vector<int>> graph(n);
	for (auto &edge : edges) {
		input.read(edge.from);
		input.read(edge.to);
		input.read(edge.cost);
		graph[edge.from].push_back(edge.to);
	}
	std::vector<bool> reachable(n);
	std::vector<int> order{source};
	reachable[source] = true;
	for (std::size_t i = 0; i < order.size(); ++i) for (int to : graph[order[i]])
		if (!reachable[to]) reachable[to] = true, order.push_back(to);
	DifferenceConstraints<> system(n);
	system.reserve(m);
	for (auto edge : edges) if (reachable[edge.from]) system.add_le(edge.from, edge.to, edge.cost);
	auto result = system.solve();
	if (!result.feasible()) {
		output.write("NEGATIVE CYCLE\n");
		return 0;
	}
	auto bounds = result.upper_bounds(source);
	for (auto bound : bounds) {
		if (bound) {
			output.write(*bound);
			output.write('\n');
		} else output.write("INF\n");
	}
}