cp-library
競技プログラミング用 C++ ライブラリ
test/hld_path_composite.test.cpp
test/hld_path_composite.test.cpp · GitHub で見る
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コード
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_set_path_composite"
#include "../tree/path_product.hpp"
#include "../tree/hld.hpp"
#include "../math/mint.hpp"
#include "components/fast_io_bulk.hpp"
#include <vector>
struct S {
mint a, b, reverse_b;
};
inline S op(S x, S y) { return {x.a * y.a, x.b * y.a + y.b, y.reverse_b * x.a + x.reverse_b}; }
inline S e() { return {1, 0, 0}; }
int main() {
FastInput input;
FastOutput output;
int n, q;
input.read(n), input.read(q);
std::vector<S> values(n);
std::size_t position = 0;
read_unsigned_records<2>(input, n, [&](unsigned a, unsigned b) { values[position++] = {a, b, b}; });
HLD tree(n);
read_unsigned_records<2>(input, n - 1, [&](unsigned u, unsigned v) { tree.add_edge(u, v); });
tree.build();
TreePathProduct<S, op, e, [](S value) {
std::swap(value.b, value.reverse_b);
return value;
}> seg(tree, values);
read_unsigned_records<4>(input, q, [&](unsigned type, unsigned u, unsigned a, unsigned b) {
if (type == 0) seg.set(u, {a, b, b});
else {
auto x = seg.apply(u, a, mint(b), [](const S& f, mint value) { return f.a * value + f.b; });
output.println(x.val());
}
});
}
#line 1 "test/hld_path_composite.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_set_path_composite"
#line 1 "tree/path_product.hpp"
#line 1 "tree/hld.hpp"
#include <algorithm>
#include <array>
#include <cassert>
#include <cstddef>
#include <limits>
#include <utility>
#include <vector>
class HLD {
int shape_ = 0, center_ = 0;
struct Node { int position, head, parent, offset; };
std::vector<Node> nodes;
void check([[maybe_unused]] int v) const { assert(0 <= v && v < n && int(in.size()) == n); }
void initialize() {
depth.assign(n, 0);
size.assign(n, 1);
heavy.assign(n, -1);
head.resize(n), in.resize(n), out.resize(n), order.resize(n);
nodes.resize(n);
shape_ = center_ = 0;
}
void finish(int root) {
in[root] = 0, out[root] = n, head[root] = root;
for (int i = n - 2; i >= 0; --i) {
int v = order[i], p = parent[v];
depth[v] = depth[p] + 1;
if (heavy[p] == v) in[v] = in[p] + 1, head[v] = head[p];
else in[v] = out[p] -= size[v], head[v] = v;
out[v] = in[v] + size[v];
}
for (int v = 0; v < n; ++v) out[v] = in[v] + size[v], order[in[v]] = v;
parent[root] = -1;
for (int v = 0; v < n; ++v) nodes[v] = {in[v], in[head[v]], parent[head[v]], depth[v] - in[v]};
}
public:
struct Segment {
int l, r;
bool reversed;
};
int n;
std::vector<std::pair<int, int>> edges;
std::vector<int> parent, depth, size, heavy, head, in, out, order;
explicit HLD(int n = 0) : n(n) {
assert(0 <= n && n <= std::numeric_limits<int>::max() / 2);
edges.reserve(std::max(0, n - 1));
}
int add_edge(int u, int v) {
assert(0 <= u && u < n && 0 <= v && v < n);
edges.emplace_back(u, v);
return int(edges.size()) - 1;
}
void build(int root = 0) {
assert(n >= 0 && edges.size() == std::size_t(std::max(0, n - 1)));
assert(!n || (0 <= root && root < n));
parent.assign(n, -1);
initialize();
if (!n) return;
std::vector<int> degree(n), neighbors(n);
for (auto [u, v] : edges) {
++degree[u], ++degree[v];
neighbors[u] ^= v, neighbors[v] ^= u;
}
center_ = int(std::max_element(degree.begin(), degree.end()) - degree.begin());
shape_ = degree[center_] <= 2 ? 1 : degree[center_] == n - 1 ? 2 : 0;
degree[root] += 2;
int count = 0;
for (int v = 0; v < n; ++v) if (degree[v] == 1) order[count++] = v;
for (int i = 0; i < count; ++i) {
int v = order[i], p = neighbors[v];
parent[v] = p;
size[p] += size[v];
if (heavy[p] == -1 || size[heavy[p]] < size[v]) heavy[p] = v;
neighbors[p] ^= v;
if (--degree[p] == 1) order[count++] = p;
}
assert(count == n - 1);
finish(root);
}
void build_from_parents(std::vector<int> parents) {
assert(parents.size() <= std::size_t(std::numeric_limits<int>::max() / 2));
n = static_cast<int>(parents.size());
parent = std::move(parents);
initialize();
edges.clear();
edges.reserve(std::max(0, n - 1));
if (!n) return;
std::fill(out.begin(), out.end(), 0);
int root = -1;
bool ordered = true;
for (int v = 0; v < n; ++v) {
int p = parent[v];
assert(-1 <= p && p < n && p != v);
if (p == -1) {
assert(root == -1);
root = v;
} else {
++out[p];
edges.emplace_back(p, v);
ordered &= p < v;
}
}
assert(root != -1);
int maximum = 0;
for (int v = 0; v < n; ++v) {
int degree = out[v] + (v != root);
if (degree > maximum) maximum = degree, center_ = v;
}
shape_ = maximum <= 2 ? 1 : maximum == n - 1 ? 2 : 0;
if (ordered) {
for (int v = n - 1; v > 0; --v) {
int p = parent[v];
size[p] += size[v];
if (heavy[p] == -1 || size[heavy[p]] < size[v]) heavy[p] = v;
order[n - 1 - v] = v;
}
} else {
int count = 0;
for (int v = 0; v < n; ++v) if (!out[v] && v != root) order[count++] = v;
for (int i = 0; i < count; ++i) {
int v = order[i], p = parent[v];
size[p] += size[v];
if (heavy[p] == -1 || size[heavy[p]] < size[v]) heavy[p] = v;
if (!--out[p] && p != root) order[count++] = p;
}
assert(count == n - 1);
}
finish(root);
}
int lca(int u, int v) const {
check(u), check(v);
if (shape_ == 1) return head[u] != head[v] ? order[0] : in[u] < in[v] ? u : v;
if (shape_ == 2) return u == v ? u : u == order[0] || v == order[0] ? order[0] : center_;
while (nodes[u].head != nodes[v].head) {
if (nodes[u].position > nodes[v].position) u = nodes[u].parent;
else v = nodes[v].parent;
}
return nodes[u].position < nodes[v].position ? u : v;
}
int dist(int u, int v) const {
int w = lca(u, v);
return depth[u] + depth[v] - 2 * depth[w];
}
bool is_ancestor(int u, int v) const {
check(u), check(v);
return in[u] <= in[v] && in[v] < out[u];
}
int ancestor(int v, int k) const {
check(v);
if (shape_) {
if (k < 0 || k > depth[v]) return -1;
if (!k) return v;
if (k == depth[v]) return order[0];
return shape_ == 2 ? parent[v] : order[in[v] - k];
}
if (k < 0) return -1;
int target = nodes[v].position + nodes[v].offset - k;
if (target < 0) return -1;
while (nodes[v].head + nodes[v].offset > target) v = nodes[v].parent;
return order[target - nodes[v].offset];
}
int jump(int u, int v, int k) const {
check(u), check(v);
if (k < 0) return -1;
if (!k) return u;
if (shape_ == 1) {
if (head[u] == head[v]) {
int delta = in[v] - in[u];
if (k > (delta < 0 ? -delta : delta)) return -1;
return order[in[u] + (delta < 0 ? -k : k)];
}
int a = depth[u], b = depth[v];
if (k > a + b) return -1;
if (k == a) return order[0];
return k < a ? order[in[u] - k] : order[in[v] - (a + b - k)];
}
if (shape_ == 2) {
int d = (u != center_) + (v != center_);
if (u == v || k > d) return -1;
return k == d ? v : center_;
}
int from = u, to = v, target = nodes[u].position + nodes[u].offset - k;
while (nodes[u].head != nodes[v].head) {
if (nodes[u].position > nodes[v].position) {
if (nodes[u].head + nodes[u].offset <= target) return order[target - nodes[u].offset];
u = nodes[u].parent;
} else v = nodes[v].parent;
}
int w = nodes[u].position < nodes[v].position ? u : v;
int d = nodes[w].position + nodes[w].offset;
int length = nodes[from].position + nodes[from].offset + nodes[to].position + nodes[to].offset - 2 * d;
if (k > length) return -1;
if (target >= d) return order[target - nodes[u].offset];
return ancestor(to, length - k);
}
std::pair<int, int> subtree(int v, bool edge = false) const {
check(v);
return {in[v] + edge, out[v]};
}
int edge_vertex(int id) const {
assert(0 <= id && id < int(edges.size()));
auto [u, v] = edges[id];
check(u);
return parent[u] == v ? u : v;
}
template <class F>
void for_each_path(int u, int v, F &&f, bool edge = false) const {
check(u), check(v);
if (shape_ == 1) {
int x = in[u], y = in[v];
if (head[u] == head[v]) {
int l = std::min(x, y) + edge, r = std::max(x, y) + 1;
if (l < r) f(l, r, x > y);
} else if (head[u] == order[0]) {
if (edge < x + 1) f(int(edge), x + 1, true);
f(in[head[v]], y + 1, false);
} else {
f(in[head[u]], x + 1, true);
if (edge < y + 1) f(int(edge), y + 1, false);
}
return;
}
std::array<std::array<int, 2>, 32> right;
int count = 0;
while (nodes[u].head != nodes[v].head) {
if (nodes[u].position > nodes[v].position) {
f(nodes[u].head, nodes[u].position + 1, true);
u = nodes[u].parent;
} else {
assert(count < int(right.size()));
right[count++] = {nodes[v].head, nodes[v].position + 1};
v = nodes[v].parent;
}
}
bool reversed = nodes[u].position > nodes[v].position;
int l = std::min(nodes[u].position, nodes[v].position) + edge, r = std::max(nodes[u].position, nodes[v].position) + 1;
if (l < r) f(l, r, reversed);
while (count) {
auto [a, b] = right[--count];
f(a, b, false);
}
}
std::vector<Segment> path(int u, int v, bool edge = false) const {
std::vector<Segment> result;
for_each_path(u, v, [&](int l, int r, bool reversed) { result.push_back({l, r, reversed}); }, edge);
return result;
}
};
#line 5 "tree/path_product.hpp"
#include <bit>
#include <cstdint>
#include <type_traits>
template<class S, auto op, auto e, auto reverse = nullptr> class TreePathProduct {
static constexpr bool has_reverse = !std::is_same_v<decltype(reverse), std::nullptr_t>;
struct Empty {};
struct Back { S prod, prefix; };
using BackStorage = std::conditional_t<has_reverse, Empty, Back>;
struct alignas(64) Node {
int left = 0, right = 0, parent = 0, head = 0, up = 0;
unsigned char priority = 0;
S value, prod, prefix;
[[no_unique_address]] BackStorage back;
static BackStorage make_back(const S& value) {
if constexpr (has_reverse) return {};
else return {value, value};
}
explicit Node(const S& v) : value(v), prod(v), prefix(v), back(make_back(v)) {}
};
std::vector<Node> nodes_;
std::vector<int> index_;
std::vector<S> dense_;
std::vector<int> dense_heads_, dense_up_;
unsigned base_ = 1;
bool flat_ = false;
int index(int v) const {
assert(0 <= v && v < size());
return index_[v];
}
void pull(int v) {
auto& node = nodes_[v];
node.prefix = node.left ? op(nodes_[node.left].prod, node.value) : node.value;
node.prod = node.right ? op(node.prefix, nodes_[node.right].prod) : node.prefix;
if constexpr (!has_reverse) {
node.back.prefix = node.left ? op(node.value, nodes_[node.left].back.prod) : node.value;
node.back.prod = node.right ? op(nodes_[node.right].back.prod, node.back.prefix) : node.back.prefix;
}
}
S back_prod(int v) const {
if constexpr (has_reverse) return reverse(nodes_[v].prod);
else return nodes_[v].back.prod;
}
S back_prefix(int v) const {
if constexpr (has_reverse) return reverse(nodes_[v].prefix);
else return nodes_[v].back.prefix;
}
template<bool Reverse> S dense_interval(int l, int r) const {
unsigned a = base_ + unsigned(l - 1), b = base_ + unsigned(r);
S left = e(), right = e();
while (a < b) {
if (a & 1) left = op(left, dense_[a++]);
if (b & 1) right = op(dense_[--b], right);
a >>= 1, b >>= 1;
}
S result = op(left, right);
if constexpr (Reverse && has_reverse) return reverse(result);
else return result;
}
template<bool Reverse> S prefix(int v) const {
S result = e();
int last = v;
for (; v; v = nodes_[v].parent) if (v <= last) {
if constexpr (Reverse) result = op(result, back_prefix(v));
else result = op(nodes_[v].prefix, result);
}
return result;
}
template<bool Reverse> S interval(int l, int r) const {
int a = l, b = r;
S left = e(), right = e();
while (a != b) {
if (nodes_[a].priority < nodes_[b].priority) {
if (l <= a) {
const auto& node = nodes_[a];
if constexpr (Reverse) left = op(op(back_prod(node.right), node.value), left);
else left = op(left, op(node.value, nodes_[node.right].prod));
}
a = nodes_[a].parent;
} else {
if (b <= r) {
if constexpr (Reverse) right = op(right, back_prefix(b));
else right = op(nodes_[b].prefix, right);
}
b = nodes_[b].parent;
}
}
if constexpr (Reverse) return op(right, op(nodes_[a].value, left));
else return op(left, op(nodes_[a].value, right));
}
template<bool Reverse, class X, class Apply> X apply_interval(int l, int r, X value, Apply& mapping) const {
int a = l, b = r;
S outside = e();
while (a != b) {
if (nodes_[a].priority < nodes_[b].priority) {
if (l <= a) {
const auto& node = nodes_[a];
if constexpr (Reverse) outside = op(op(back_prod(node.right), node.value), outside);
else value = mapping(nodes_[node.right].prod, mapping(node.value, std::move(value)));
}
a = nodes_[a].parent;
} else {
if (b <= r) {
if constexpr (Reverse) value = mapping(back_prefix(b), std::move(value));
else outside = op(nodes_[b].prefix, outside);
}
b = nodes_[b].parent;
}
}
return mapping(outside, mapping(nodes_[a].value, std::move(value)));
}
template<class X, class Apply> X dense_apply(int u, int v, X value, Apply& mapping) const {
std::array<std::pair<int, int>, 4> right;
int count = 0;
while (dense_heads_[u] != dense_heads_[v]) {
if (dense_heads_[u] > dense_heads_[v]) {
value = mapping(dense_interval<true>(dense_heads_[u], u), std::move(value));
u = dense_up_[u];
} else {
assert(count < int(right.size()));
right[count++] = {dense_heads_[v], v};
v = dense_up_[v];
}
}
if (u <= v) value = mapping(dense_interval<false>(u, v), std::move(value));
else value = mapping(dense_interval<true>(v, u), std::move(value));
while (count) {
auto [l, r] = right[--count];
value = mapping(dense_interval<false>(l, r), std::move(value));
}
return value;
}
public:
TreePathProduct() = default;
TreePathProduct(const HLD& tree, const std::vector<S>& values) { build(tree, values); }
void build(const HLD& tree, const std::vector<S>& values) {
assert(values.size() == std::size_t(tree.n) && tree.order.size() == values.size());
index_.resize(values.size());
nodes_.clear();
for (int v : tree.order) index_[v] = tree.in[v] + 1;
flat_ = false;
dense_.clear();
if constexpr (has_reverse) {
std::vector<unsigned char> levels(values.size());
unsigned maximum = 0;
for (int v : tree.order) {
if (tree.parent[v] != -1) levels[v] = levels[tree.parent[v]] + (tree.head[v] == v);
maximum = std::max(maximum, unsigned(levels[v]));
}
flat_ = maximum <= 4;
}
if (flat_) {
base_ = std::bit_ceil(unsigned(size()) ? unsigned(size()) : 1U);
dense_.assign(std::size_t(base_) * 2, e());
dense_heads_.assign(values.size() + 1, 0), dense_up_.assign(values.size() + 1, 0);
for (int v : tree.order) {
int id = index_[v], h = tree.head[v];
dense_heads_[id] = index_[h];
dense_up_[id] = tree.parent[h] == -1 ? 0 : index_[tree.parent[h]];
dense_[base_ + unsigned(id - 1)] = values[v];
}
for (unsigned i = base_ - 1; i; --i) dense_[i] = op(dense_[i * 2], dense_[i * 2 + 1]);
return;
}
dense_heads_.clear(), dense_up_.clear();
nodes_.reserve(values.size() + 1);
nodes_.emplace_back(e());
for (int v : tree.order) nodes_.emplace_back(values[v]);
std::vector<int> stack, order;
order.reserve(values.size());
for (int v : tree.order) {
if (tree.head[v] != v) continue;
stack.clear();
unsigned position = 0;
int head = index_[v], up = tree.parent[v] == -1 ? 0 : index_[tree.parent[v]];
for (int u = v; u != -1; u = tree.heavy[u]) {
int id = index_[u], weight = tree.size[u] - (tree.heavy[u] == -1 ? 0 : tree.size[tree.heavy[u]]);
auto& node = nodes_[id];
node.head = head, node.up = up;
node.priority = std::bit_width(position ^ (position + unsigned(weight)));
position += unsigned(weight);
int last = 0;
while (!stack.empty() && nodes_[stack.back()].priority < node.priority) {
last = stack.back();
stack.pop_back();
}
node.left = last;
if (last) nodes_[last].parent = id;
if (!stack.empty()) nodes_[stack.back()].right = id, node.parent = stack.back();
stack.push_back(id);
}
order.push_back(stack[0]);
}
for (std::size_t i = 0; i < order.size(); ++i) {
const auto& node = nodes_[order[i]];
if (node.left) order.push_back(node.left);
if (node.right) order.push_back(node.right);
}
for (auto it = order.rbegin(); it != order.rend(); ++it) pull(*it);
}
int size() const { return int(index_.size()); }
bool empty() const { return index_.empty(); }
const S& get(int v) const {
int id = index(v);
return flat_ ? dense_[base_ + unsigned(id - 1)] : nodes_[id].value;
}
void set(int v, const S& value) {
int id = index(v);
if (flat_) {
unsigned k = base_ + unsigned(id - 1);
dense_[k] = value;
for (k >>= 1; k; k >>= 1) dense_[k] = op(dense_[k * 2], dense_[k * 2 + 1]);
return;
}
nodes_[id].value = value;
for (; id; id = nodes_[id].parent) pull(id);
}
S prod(int u, int v) const {
u = index(u), v = index(v);
if (flat_) {
auto append = [](const S& part, S value) { return op(std::move(value), part); };
return dense_apply(u, v, e(), append);
}
S left = e(), right = e();
while (nodes_[u].head != nodes_[v].head) {
if (nodes_[u].head > nodes_[v].head) {
left = op(left, prefix<true>(u));
u = nodes_[u].up;
} else {
right = op(prefix<false>(v), right);
v = nodes_[v].up;
}
}
S middle = u <= v ? interval<false>(u, v) : interval<true>(v, u);
return op(left, op(middle, right));
}
template<class X, class Apply> X apply(int u, int v, X value, Apply mapping) const {
u = index(u), v = index(v);
if (flat_) return dense_apply(u, v, std::move(value), mapping);
S right = e();
while (nodes_[u].head != nodes_[v].head) {
if (nodes_[u].head > nodes_[v].head) {
for (int id = u; id; id = nodes_[id].parent)
if (id <= u) value = mapping(back_prefix(id), std::move(value));
u = nodes_[u].up;
} else {
right = op(prefix<false>(v), right);
v = nodes_[v].up;
}
}
if (u <= v) value = apply_interval<false>(u, v, std::move(value), mapping);
else value = apply_interval<true>(v, u, std::move(value), mapping);
return mapping(right, std::move(value));
}
};
#line 1 "math/mint.hpp"
#line 4 "math/mint.hpp"
#include <istream>
#include <ostream>
#line 7 "math/mint.hpp"
#if defined(__GNUC__) && !defined(__clang__) && (defined(__x86_64__) || defined(__i386__))
#pragma GCC push_options
#pragma GCC optimize("O3")
#endif
namespace mint_detail {
template <class I>
constexpr bool mint_integral = std::is_integral_v<I>
#if defined(__SIZEOF_INT128__)
|| std::is_same_v<I, __int128> || std::is_same_v<I, unsigned __int128>
#endif
;
struct [[gnu::warn_unused]] Mint {
using mint = Mint;
unsigned v = 0;
[[nodiscard]] static constexpr unsigned mod() { return 998244353; }
[[nodiscard, gnu::always_inline]] static unsigned reduce(unsigned long long x) {
return (x + (unsigned long long)(unsigned(x) * 998244351u) * mod()) >> 32;
}
[[gnu::always_inline]] Mint() = default;
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
Mint(I x) {
long long r = x % (long long)mod();
if (r < 0) r += mod();
v = reduce((unsigned long long)r * 932051910);
}
[[nodiscard, gnu::always_inline]] static Mint raw(unsigned x) {
Mint a;
a.v = reduce((unsigned long long)x * 932051910);
return a;
}
[[nodiscard, gnu::always_inline]] static Mint word(unsigned x) {
Mint a;
a.v = x;
return a;
}
[[nodiscard, gnu::always_inline]] unsigned val() const {
unsigned r = reduce(v);
return r < mod() ? r : r - mod();
}
friend std::istream &operator>>(std::istream &is, Mint &x) {
long long value;
if (is >> value) x = Mint(value);
return is;
}
friend std::ostream &operator<<(std::ostream &os, const Mint &x) {
return os << x.val();
}
[[gnu::always_inline]] Mint &operator+=(Mint b) {
v += b.v;
if (v >= 2 * mod()) v -= 2 * mod();
return *this;
}
[[gnu::always_inline]] Mint &operator-=(Mint b) {
v -= b.v;
if (v >> 31) v += 2 * mod();
return *this;
}
[[gnu::always_inline]] Mint &operator*=(Mint b) {
v = reduce((unsigned long long)v * b.v);
return *this;
}
Mint &operator/=(Mint b) { return *this *= b.inv(); }
Mint &operator++() { return *this += Mint(1); }
Mint &operator--() { return *this -= Mint(1); }
Mint operator++(int) {
Mint a = *this;
++*this;
return a;
}
Mint operator--(int) {
Mint a = *this;
--*this;
return a;
}
[[nodiscard, gnu::always_inline]] Mint operator+() const { return *this; }
[[nodiscard, gnu::always_inline]] Mint operator-() const { return word(v ? 2 * mod() - v : 0); }
[[nodiscard, gnu::always_inline]] Mint operator+(Mint b) const { return Mint(*this) += b; }
[[nodiscard, gnu::always_inline]] Mint operator-(Mint b) const { return Mint(*this) -= b; }
[[nodiscard, gnu::always_inline]] Mint operator*(Mint b) const { return Mint(*this) *= b; }
[[nodiscard]] Mint operator/(Mint b) const { return Mint(*this) /= b; }
[[nodiscard, gnu::always_inline]] bool operator==(Mint b) const { return (v < mod() ? v : v - mod()) == (b.v < mod() ? b.v : b.v - mod()); }
[[nodiscard, gnu::always_inline]] bool operator!=(Mint b) const { return !(*this == b); }
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
[[nodiscard]] friend Mint operator+(I a, Mint b) { return Mint(a) + b; }
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
[[nodiscard]] friend Mint operator-(I a, Mint b) { return Mint(a) - b; }
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
[[nodiscard]] friend Mint operator*(I a, Mint b) { return Mint(a) * b; }
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
[[nodiscard]] friend Mint operator/(I a, Mint b) { return Mint(a) / b; }
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
[[nodiscard]] friend bool operator==(I a, Mint b) { return Mint(a) == b; }
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
[[nodiscard]] friend bool operator!=(I a, Mint b) { return Mint(a) != b; }
[[nodiscard]] Mint pow(long long n) const {
assert(n >= 0);
if (!n) return Mint(1);
Mint r(1), a = *this;
for (; n > 1; n >>= 1, a *= a)
if (n & 1) r *= a;
return r * a;
}
[[nodiscard, gnu::noinline]] Mint inv() const {
assert(*this != Mint(0));
Mint a2 = *this * *this, a3 = a2 * *this;
Mint a7 = a3 * a3 * *this;
Mint a31 = a7;
for (int i = 0; i < 2; ++i) a31 *= a31;
a31 *= a3;
Mint r = a7;
for (int i = 0; i < 3; ++i) r *= r;
r *= a3;
r *= r;
for (int j = 0; j < 4; ++j) {
for (int i = 0; i < 5; ++i) r *= r;
r *= a31;
}
for (int i = 0; i < 3; ++i) r *= r;
return r * a7;
}
};
} // namespace mint_detail
using mint = mint_detail::Mint;
using fps_mint = mint;
#if defined(__GNUC__) && !defined(__clang__) && (defined(__x86_64__) || defined(__i386__))
#pragma GCC pop_options
#endif
#line 1 "components/fast_io_bulk.hpp"
#line 1 "components/fast_io_output.hpp"
#line 1 "components/fast_io.hpp"
#line 8 "components/fast_io.hpp"
#include <charconv>
#line 11 "components/fast_io.hpp"
#include <cstdio>
#include <cstring>
#include <memory>
#include <stdexcept>
#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 7 "components/fast_io_output.hpp"
namespace fast_io_detail {
struct BulkOutput {
static char *small(char *out, std::uint32_t value) {
unsigned n = 1 + (value >= 10) + (value >= 100) + (value >= 1000);
if constexpr (std::endian::native == std::endian::little) {
std::uint32_t word;
std::memcpy(&word, FastOutput::quads[value].data(), 4);
word >>= (4 - n) * 8;
std::memcpy(out, &word, 4);
} else std::memcpy(out, FastOutput::quads[value].data() + 4 - n, n);
return out + n;
}
static char *number(char *out, std::uint32_t value) {
if (value >= 100000000) {
out = small(out, value / 100000000);
value %= 100000000;
std::memcpy(out, FastOutput::quads[value / 10000].data(), 4);
std::memcpy(out + 4, FastOutput::quads[value % 10000].data(), 4);
return out + 8;
}
if (value >= 10000) {
out = small(out, value / 10000);
std::memcpy(out, FastOutput::quads[value % 10000].data(), 4);
return out + 4;
}
return small(out, value);
}
template<std::size_t Fields, class Read>
#if defined(__GNUC__) || defined(__clang__)
[[gnu::noinline]]
#endif
static void records(FastOutput &out, std::size_t count, Read read) {
constexpr auto bytes = 11 * Fields;
constexpr auto block = std::max<std::size_t>(1, (1 << 16) / bytes);
for (std::size_t base = 0; base < count;) {
const auto n = std::min(count - base, block);
char *begin = out.reserve(n * bytes), *p = begin;
for (std::size_t i = 0; i < n; ++i) {
auto values = read(base + i);
for (std::size_t j = 0; j < Fields; ++j) {
p = number(p, std::uint32_t(values[j]));
*p++ = j + 1 == Fields ? '\n' : ' ';
}
}
out.length += p - begin;
base += n;
}
}
static void write(FastOutput &out, std::string_view text) {
if (text.size() <= (1 << 16)) return out.write(text);
if (out.length && !out.flush()) throw std::runtime_error("output failed");
std::size_t done = 0;
while (done < text.size()) {
const auto written = std::fwrite(text.data() + done, 1, text.size() - done, out.file);
if (!written) throw std::runtime_error("output failed");
done += written;
}
}
};
}
template<std::size_t Fields, class Read>
void write_unsigned_records(FastOutput &output, std::size_t count, Read read) {
static_assert(Fields > 0 && Fields <= std::numeric_limits<std::size_t>::max() / 11);
fast_io_detail::BulkOutput::records<Fields>(output, count, std::move(read));
}
#line 6 "components/fast_io_bulk.hpp"
#include <span>
#line 8 "components/fast_io_bulk.hpp"
#if defined(__linux__) && defined(__x86_64__) && defined(__GNUC__) && !defined(__clang__)
#include <immintrin.h>
#pragma GCC push_options
_Pragma("GCC target(\"avx2\")")
#pragma GCC optimize("O3")
namespace fast_io_detail {
struct BulkInput {
alignas(32) static inline constexpr auto rows = [] {
std::array<std::array<unsigned char, 16>, 11> r{};
for (int n = 0; n <= 10; ++n)
for (int i = 0; i < 16; ++i) r[n][i] = i < 16 - n ? 128 : i - (16 - n);
return r;
}();
static constexpr std::size_t kChunk = 1 << 17, kCapacity = kChunk / 4 + 66;
static unsigned separators(__m256i bytes) {
return unsigned(_mm256_movemask_epi8(_mm256_cmpeq_epi8(_mm256_max_epu8(bytes, _mm256_set1_epi8(' ')), _mm256_set1_epi8(' '))));
}
[[gnu::always_inline]] static __m256i two(const char *&p, __m256i &invalid) {
const auto bytes = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(p));
const unsigned sep = separators(bytes), a = std::countr_zero(sep), b = std::countr_zero(sep & (sep - 1));
if (a < 1 || a > 10 || b <= a + 1 || b - a - 1 > 10) [[unlikely]] {
invalid = _mm256_set1_epi32(-1);
p += std::min(b + 1, 32u);
return _mm256_setzero_si256();
}
const auto window = _mm256_inserti128_si256(bytes, _mm_loadu_si128(reinterpret_cast<const __m128i *>(p + a + 1)), 1);
const auto control = _mm256_set_m128i(_mm_loadu_si128(reinterpret_cast<const __m128i *>(rows[b - a - 1].data())),
_mm_loadu_si128(reinterpret_cast<const __m128i *>(rows[a].data())));
const auto digits = _mm256_shuffle_epi8(_mm256_sub_epi8(window, _mm256_set1_epi8('0')), control);
invalid = _mm256_or_si256(invalid, _mm256_subs_epu8(digits, _mm256_set1_epi8(9)));
p += b + 1;
return _mm256_madd_epi16(_mm256_maddubs_epi16(digits, _mm256_set1_epi16(0x010a)), _mm256_set1_epi32(0x00010064));
}
static std::uint32_t one(const char *&p, bool &bad) {
const auto bytes = _mm_loadu_si128(reinterpret_cast<const __m128i *>(p));
const auto spaces = _mm_cmpeq_epi8(_mm_max_epu8(bytes, _mm_set1_epi8(' ')), _mm_set1_epi8(' '));
const unsigned n = std::countr_zero(unsigned(_mm_movemask_epi8(spaces)) | 0x10000u);
if (n < 1 || n > 10) [[unlikely]] {
bad = true;
p += std::min(n + 1, 16u);
return 0;
}
const auto digits = _mm_shuffle_epi8(_mm_sub_epi8(bytes, _mm_set1_epi8('0')),
_mm_loadu_si128(reinterpret_cast<const __m128i *>(rows[n].data())));
const auto invalid = _mm_subs_epu8(digits, _mm_set1_epi8(9));
bad |= !_mm_testz_si128(invalid, invalid);
const auto groups = _mm_madd_epi16(_mm_maddubs_epi16(digits, _mm_set1_epi16(0x010a)), _mm_set1_epi32(0x00010064));
const auto halves = _mm_madd_epi16(_mm_packus_epi32(groups, groups), _mm_set1_epi32(0x00012710));
const std::uint64_t value = std::uint64_t(unsigned(_mm_cvtsi128_si32(halves))) * 100000000 + unsigned(_mm_extract_epi32(halves, 1));
bad |= value > 0xffffffffULL;
p += n + 1;
return std::uint32_t(value);
}
static const char *after_separator(const char *p) {
const unsigned mask = separators(_mm256_loadu_si256(reinterpret_cast<const __m256i *>(p)));
return mask ? p + std::countr_zero(mask) + 1 : nullptr;
}
static std::size_t lockstep(const char *(&streams)[4], const char *const (&end)[4], unsigned *const (&out)[4], __m256i &invalid) {
const char *p[4] = {streams[0], streams[1], streams[2], streams[3]};
std::size_t done = 0;
for (;;) {
std::ptrdiff_t left = end[0] - p[0];
for (int k = 1; k < 4; ++k) left = std::min(left, end[k] - p[k]);
const auto steps = std::min(left / 33, std::ptrdiff_t((kCapacity - done) / 2));
if (steps <= 0) break;
for (auto j = steps; j; --j, done += 2) {
const auto g0 = two(p[0], invalid), g1 = two(p[1], invalid), g2 = two(p[2], invalid), g3 = two(p[3], invalid);
const auto k = _mm256_set1_epi32(0x00012710);
const auto h01 = _mm256_castsi256_ps(_mm256_madd_epi16(_mm256_packus_epi32(g0, g1), k));
const auto h23 = _mm256_castsi256_ps(_mm256_madd_epi16(_mm256_packus_epi32(g2, g3), k));
const auto high = _mm256_castps_si256(_mm256_shuffle_ps(h01, h23, 0x88));
const auto low = _mm256_castps_si256(_mm256_shuffle_ps(h01, h23, 0xdd));
const auto overflow = _mm256_or_si256(_mm256_cmpgt_epi32(high, _mm256_set1_epi32(42)),
_mm256_and_si256(_mm256_cmpeq_epi32(high, _mm256_set1_epi32(42)), _mm256_cmpgt_epi32(low, _mm256_set1_epi32(94967295))));
invalid = _mm256_or_si256(invalid, overflow);
const auto value = _mm256_add_epi32(_mm256_mullo_epi32(high, _mm256_set1_epi32(100000000)), low);
const auto q = _mm256_permutevar8x32_epi32(value, _mm256_setr_epi32(0, 4, 1, 5, 2, 6, 3, 7));
const auto q01 = _mm256_castsi256_si128(q), q23 = _mm256_extracti128_si256(q, 1);
_mm_storel_epi64(reinterpret_cast<__m128i *>(out[0] + done), q01);
_mm_storeh_pd(reinterpret_cast<double *>(out[1] + done), _mm_castsi128_pd(q01));
_mm_storel_epi64(reinterpret_cast<__m128i *>(out[2] + done), q23);
_mm_storeh_pd(reinterpret_cast<double *>(out[3] + done), _mm_castsi128_pd(q23));
}
}
for (int k = 0; k < 4; ++k) streams[k] = p[k];
return done;
}
template <class Emit>
static std::size_t chunk_blocks(const char *&p, const char *limit, std::size_t count, unsigned *const (&out)[4], Emit &&emit) {
const auto bytes = std::min({kChunk, 2 * (count - 32), std::size_t(limit - p) - 64}) & ~std::size_t(3);
const std::size_t stream = bytes / 4;
const char *p1 = after_separator(p + stream), *p2 = after_separator(p + 2 * stream);
const char *p3 = after_separator(p + 3 * stream), *last = after_separator(p + bytes);
if (!p1 || !p2 || !p3 || !last) return 0;
const char *s[4] = {p, p1, p2, p3}, *const end[4] = {p1, p2, p3, last};
auto invalid = _mm256_setzero_si256();
const auto done = lockstep(s, end, out, invalid);
bool bad = !_mm256_testz_si256(invalid, invalid);
std::size_t n[4];
for (int k = 0; k < 4; ++k) {
n[k] = done;
while (s[k] < end[k] && n[k] < kCapacity) out[k][n[k]++] = one(s[k], bad);
bad |= s[k] != end[k];
}
const auto parsed = n[0] + n[1] + n[2] + n[3];
if (bad || parsed > count) return 0;
for (int k = 0; k < 4; ++k) emit(out[k], n[k]);
p = last;
return parsed;
}
static std::size_t chunk(const char *&p, const char *limit, unsigned *dst, std::size_t count, unsigned *scratch) {
unsigned *const out[4] = {dst, scratch, scratch + kCapacity, scratch + 2 * kCapacity};
bool first = true;
unsigned *next = dst;
return chunk_blocks(p, limit, count, out, [&](const unsigned *values, std::size_t n) {
if (!first) std::memcpy(next, values, n * sizeof(unsigned));
first = false;
next += n;
});
}
template <class Emit>
static void read_blocks(FastInput &in, std::size_t count, Emit emit) {
std::unique_ptr<unsigned[]> scratch;
std::size_t done = 0;
bool chunks = true;
while (done < count) {
const char *p = in.current;
while (p != in.end && static_cast<unsigned char>(*p) <= ' ') ++p;
while (chunks && count - done >= 1024 && in.end - p >= 1088) {
if (!scratch) scratch = std::make_unique_for_overwrite<unsigned[]>(4 * kCapacity);
unsigned *const out[4] = {scratch.get(), scratch.get() + kCapacity, scratch.get() + 2 * kCapacity, scratch.get() + 3 * kCapacity};
const auto parsed = chunk_blocks(p, in.end, count - done, out, emit);
if (!parsed) {
chunks = false;
break;
}
done += parsed;
}
unsigned tail[64];
std::size_t used = 0;
while (done + 2 <= count && in.end - p >= 32) {
const char *next = p;
auto invalid = _mm256_setzero_si256();
const auto groups = two(next, invalid);
if (!_mm256_testz_si256(invalid, invalid)) break;
const auto halves = _mm256_madd_epi16(_mm256_packus_epi32(groups, groups), _mm256_set1_epi32(0x00012710));
const unsigned h0 = _mm256_extract_epi32(halves, 0), l0 = _mm256_extract_epi32(halves, 1);
const unsigned h1 = _mm256_extract_epi32(halves, 4), l1 = _mm256_extract_epi32(halves, 5);
if (h0 > 42 || (h0 == 42 && l0 > 94967295) || h1 > 42 || (h1 == 42 && l1 > 94967295)) break;
tail[used++] = h0 * 100000000 + l0;
tail[used++] = h1 * 100000000 + l1;
if (used == 64) {
emit(tail, used);
used = 0;
}
done += 2;
p = next;
}
if (used) emit(tail, used);
in.current = p;
if (done < count) {
unsigned value = 0;
in.read(value);
emit(&value, 1);
++done;
}
}
}
static void read(FastInput &in, unsigned *out, std::size_t count) {
read_blocks(in, count, [&](const unsigned *values, std::size_t n) {
std::memcpy(out, values, n * sizeof(unsigned));
out += n;
});
}
};
}
#pragma GCC pop_options
#endif
namespace fast_io_detail {
template <class Emit, std::size_t... I>
void emit_record(Emit &emit, const std::uint32_t *values, std::index_sequence<I...>) {
emit(values[I]...);
}
}
template <class Emit>
void read_unsigned_blocks(FastInput &input, std::size_t count, Emit emit) {
#if defined(__linux__) && defined(__x86_64__) && defined(__GNUC__) && !defined(__clang__)
if (__builtin_cpu_supports("avx2")) {
fast_io_detail::BulkInput::read_blocks(input, count, emit);
return;
}
#endif
std::uint32_t values[64];
while (count) {
const auto n = std::min<std::size_t>(count, 64);
for (std::size_t i = 0; i < n; ++i) input.read(values[i]);
emit(values, n);
count -= n;
}
}
inline void read_unsigned(FastInput &input, std::span<std::uint32_t> out) {
read_unsigned_blocks(input, out.size(), [&](const std::uint32_t *values, std::size_t count) {
std::memcpy(out.data(), values, count * sizeof(std::uint32_t));
out = out.subspan(count);
});
}
template <std::size_t Fields, class Emit>
void read_unsigned_records(FastInput &input, std::size_t count, Emit emit) {
static_assert(Fields > 0);
if (count > std::numeric_limits<std::size_t>::max() / Fields) throw std::length_error("input size");
std::array<std::uint32_t, Fields> pending;
std::size_t used = 0;
constexpr auto indices = std::make_index_sequence<Fields>();
read_unsigned_blocks(input, count * Fields, [&](const std::uint32_t *values, std::size_t n) {
std::size_t i = 0;
if (used) {
while (used < Fields && i < n) pending[used++] = values[i++];
if (used == Fields) {
fast_io_detail::emit_record(emit, pending.data(), indices);
used = 0;
}
}
for (; i < n && n - i >= Fields; i += Fields) fast_io_detail::emit_record(emit, values + i, indices);
while (i < n) pending[used++] = values[i++];
});
}
#line 7 "test/hld_path_composite.test.cpp"
struct S {
mint a, b, reverse_b;
};
inline S op(S x, S y) { return {x.a * y.a, x.b * y.a + y.b, y.reverse_b * x.a + x.reverse_b}; }
inline S e() { return {1, 0, 0}; }
int main() {
FastInput input;
FastOutput output;
int n, q;
input.read(n), input.read(q);
std::vector<S> values(n);
std::size_t position = 0;
read_unsigned_records<2>(input, n, [&](unsigned a, unsigned b) { values[position++] = {a, b, b}; });
HLD tree(n);
read_unsigned_records<2>(input, n - 1, [&](unsigned u, unsigned v) { tree.add_edge(u, v); });
tree.build();
TreePathProduct<S, op, e, [](S value) {
std::swap(value.b, value.reverse_b);
return value;
}> seg(tree, values);
read_unsigned_records<4>(input, q, [&](unsigned type, unsigned u, unsigned a, unsigned b) {
if (type == 0) seg.set(u, {a, b, b});
else {
auto x = seg.apply(u, a, mint(b), [](const S& f, mint value) { return f.a * value + f.b; });
output.println(x.val());
}
});
}