cp-library
競技プログラミング用 C++ ライブラリ
test/lazy_reversible_treap_affine.test.cpp
test/lazy_reversible_treap_affine.test.cpp · GitHub で見る
依存ライブラリ
コード
#define PROBLEM "https://judge.yosupo.jp/problem/dynamic_sequence_range_affine_range_sum"
#include "../data_structure/lazy_reversible_treap.hpp"
#include "../components/fast_io.hpp"
#include "../math/mint.hpp"
#include <vector>
struct F { mint a, b; };
mint op(mint a, mint b) { return a + b; }
mint e() { return 0; }
mint mapping(F f, mint s, int n) { return f.a * s + f.b * n; }
F composition(F f, F g) { return {f.a * g.a, f.a * g.b + f.b}; }
F id() { return {1, 0}; }
int main() {
FastInput input;
FastOutput output;
int n = 0, q = 0;
input.read(n); input.read(q);
std::vector<mint> a(n);
for (auto &x : a) { unsigned value = 0; input.read(value); x = mint::raw(value); }
LazyReversibleTreap<mint, op, e, F, mapping, composition, id, true> tree(a);
tree.reserve(n + q);
while (q--) {
int type = 0, l = 0;
input.read(type); input.read(l);
if (type == 0) { unsigned x = 0; input.read(x); tree.insert(l, mint::raw(x)); }
else if (type == 1) tree.erase(l);
else {
int r = 0;
input.read(r);
if (type == 2) tree.reverse(l, r);
else if (type == 3) { unsigned b = 0, c = 0; input.read(b); input.read(c); tree.apply(l, r, {mint::raw(b), mint::raw(c)}); }
else { output.write(tree.prod(l, r).val()); output.write('\n'); }
}
}
}
#line 1 "test/lazy_reversible_treap_affine.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/dynamic_sequence_range_affine_range_sum"
#line 1 "data_structure/lazy_reversible_treap.hpp"
#line 1 "components/splitmix64.hpp"
#include <cstdint>
inline std::uint64_t splitmix64(std::uint64_t x) {
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9ULL;
x = (x ^ (x >> 27)) * 0x94d049bb133111ebULL;
return x ^ (x >> 31);
}
class SplitMix64 {
std::uint64_t state;
public:
explicit SplitMix64(std::uint64_t seed = 0) : state(seed) {}
std::uint64_t operator()() { return splitmix64(state += 0x9e3779b97f4a7c15ULL); }
};
#line 5 "data_structure/lazy_reversible_treap.hpp"
#include <algorithm>
#include <cassert>
#include <cstddef>
#line 9 "data_structure/lazy_reversible_treap.hpp"
#include <type_traits>
#include <utility>
#include <vector>
#if defined(__GNUC__) && !defined(__clang__) && (defined(__x86_64__) || defined(__i386__))
#pragma GCC push_options
#pragma GCC optimize("O3")
#endif
template <class S, auto op, auto e, class F, auto mapping, auto composition, auto id, bool commutative = false>
class LazyReversibleTreap {
struct Empty {};
using Back = std::conditional_t<commutative, Empty, S>;
struct Node {
int left = 0, right = 0;
std::uint32_t count : 30 = 1;
std::uint32_t pending : 1 = 0;
std::uint32_t reversed : 1 = 0;
std::uint32_t priority;
S value, product;
[[no_unique_address]] Back back;
F lazy = id();
static Back make_back(const S &value) {
if constexpr (commutative) return {};
else return value;
}
Node(S value, std::uint32_t priority) : priority(priority), value(std::move(value)), product(this->value), back(make_back(this->value)) {}
};
std::vector<Node> t;
SplitMix64 rng;
int root = 0, free = 0;
bool lazy_applied = false;
int count(int x) const { return t[x].count; }
template <bool resize = true>
void pull(int x) {
auto &v = t[x];
int l = v.left, r = v.right;
if constexpr (resize) v.count = count(l) + count(r) + 1;
v.product = l ? op(t[l].product, v.value) : v.value;
if (r) v.product = op(std::move(v.product), t[r].product);
if constexpr (!commutative) {
v.back = r ? op(t[r].back, v.value) : v.value;
if (l) v.back = op(std::move(v.back), t[l].back);
}
}
void flip(int x) {
if (!x || count(x) == 1) return;
auto &v = t[x];
std::swap(v.left, v.right);
if constexpr (!commutative) std::swap(v.product, v.back);
v.reversed ^= 1;
}
void act(int x, const F &f) {
if (!x) return;
auto &v = t[x];
if (count(x) == 1) {
v.value = v.product = mapping(f, v.product, 1);
if constexpr (!commutative) v.back = v.product;
return;
}
v.product = mapping(f, v.product, count(x));
if constexpr (!commutative) v.back = mapping(f, v.back, count(x));
v.lazy = v.pending ? composition(f, v.lazy) : f;
v.pending = true;
}
void push(int x) {
auto &v = t[x];
if (v.reversed) {
flip(v.left);
flip(v.right);
v.reversed = 0;
}
if (v.pending) {
v.value = mapping(v.lazy, v.value, 1);
act(v.left, v.lazy);
act(v.right, v.lazy);
v.pending = false;
}
}
int make(S value) {
if (free) {
int x = free;
free = t[x].left;
t[x] = Node(std::move(value), std::uint32_t(rng()));
return x;
}
assert(t.size() <= (std::size_t(1) << 30) - 1);
t.emplace_back(std::move(value), std::uint32_t(rng()));
return int(t.size()) - 1;
}
std::pair<int, int> split(int x, int k) {
if (!x) return {0, 0};
if (!k) return {0, x};
if (k == count(x)) return {x, 0};
push(x);
int left = count(t[x].left);
if (k <= left) {
auto [a, b] = split(t[x].left, k);
t[x].left = b;
pull(x);
return {a, x};
}
auto [a, b] = split(t[x].right, k - left - 1);
t[x].right = a;
pull(x);
return {x, b};
}
int merge(int a, int b) {
if (!a || !b) return a | b;
if (t[a].priority > t[b].priority) {
push(a);
t[a].right = merge(t[a].right, b);
pull(a);
return a;
}
push(b);
t[b].left = merge(a, t[b].left);
pull(b);
return b;
}
int insert_node(int x, int p, int added) {
if (!x) return added;
if (t[added].priority >= t[x].priority) {
auto [a, b] = split(x, p);
t[added].left = a;
t[added].right = b;
pull(added);
return added;
}
push(x);
int left = count(t[x].left);
if (p <= left) t[x].left = insert_node(t[x].left, p, added);
else t[x].right = insert_node(t[x].right, p - left - 1, added);
pull(x);
return x;
}
int erase_node(int x, int p, S &value) {
push(x);
int left = count(t[x].left);
if (p == left) {
value = std::move(t[x].value);
int result = merge(t[x].left, t[x].right);
t[x].left = free;
free = x;
return result;
}
if (p < left) t[x].left = erase_node(t[x].left, p, value);
else t[x].right = erase_node(t[x].right, p - left - 1, value);
pull(x);
return x;
}
void set_node(int x, int p, S value) {
push(x);
int left = count(t[x].left);
if (p == left) t[x].value = std::move(value);
else if (p < left) set_node(t[x].left, p, std::move(value));
else set_node(t[x].right, p - left - 1, std::move(value));
pull<false>(x);
}
S fold(int x, int l, int r, bool reversed = false) const {
for (;;) {
const auto &v = t[x];
if (!l && r == count(x)) {
if constexpr (!commutative) if (reversed) return v.back;
return v.product;
}
int a = reversed ? v.right : v.left, b = reversed ? v.left : v.right;
int left = count(a);
reversed ^= v.reversed;
if (r <= left) { x = a; continue; }
if (left < l) { x = b; l -= left + 1; r -= left + 1; continue; }
S result = v.value;
if (l < left) result = op(fold(a, l, left, reversed), std::move(result));
if (left + 1 < r) result = op(std::move(result), fold(b, 0, r - left - 1, reversed));
return result;
}
}
S fold_lazy(int x, int l, int r, const F *carry = nullptr, bool reversed = false) const {
const auto &v = t[x];
if (!l && r == count(x)) {
S result = v.product;
if constexpr (!commutative) if (reversed) result = v.back;
return carry ? mapping(*carry, std::move(result), count(x)) : result;
}
F combined = id();
if (v.pending) {
combined = carry ? composition(*carry, v.lazy) : v.lazy;
carry = &combined;
}
int a = reversed ? v.right : v.left, b = reversed ? v.left : v.right;
int left = count(a);
reversed ^= v.reversed;
if (r <= left) return fold_lazy(a, l, r, carry, reversed);
if (left < l) return fold_lazy(b, l - left - 1, r - left - 1, carry, reversed);
S result = carry ? mapping(*carry, v.value, 1) : v.value;
if (l < left) result = op(fold_lazy(a, l, left, carry, reversed), std::move(result));
if (left + 1 < r) result = op(std::move(result), fold_lazy(b, 0, r - left - 1, carry, reversed));
return result;
}
void apply_node(int x, int l, int r, const F &f) {
if (!l && r == count(x)) { act(x, f); return; }
push(x);
int left = count(t[x].left);
if (l < left) apply_node(t[x].left, l, std::min(r, left), f);
if (l <= left && left < r) t[x].value = mapping(f, t[x].value, 1);
if (left + 1 < r) apply_node(t[x].right, std::max(l - left - 1, 0), r - left - 1, f);
pull<false>(x);
}
int reverse_node(int x, int l, int r) {
if (!l && r == count(x)) { flip(x); return x; }
push(x);
int left = count(t[x].left);
if (r <= left) t[x].left = reverse_node(t[x].left, l, r);
else if (left < l) t[x].right = reverse_node(t[x].right, l - left - 1, r - left - 1);
else {
auto [a, b] = split(t[x].left, l);
auto [c, d] = split(t[x].right, r - left - 1);
flip(b);
flip(c);
t[x].left = merge(a, c);
t[x].right = merge(b, d);
}
if constexpr (!commutative) pull<false>(x);
return x;
}
void collect(int x, std::vector<S> &values) {
if (!x) return;
push(x);
collect(t[x].left, values);
values.push_back(t[x].value);
collect(t[x].right, values);
}
void bounds(int l, int r) const { assert(0 <= l && l <= r && r <= size()); (void)l; (void)r; }
public:
using value_type = S;
using action_type = F;
explicit LazyReversibleTreap(std::uint64_t seed = 0) : rng(seed) { t.emplace_back(e(), 0); t[0].count = 0; }
explicit LazyReversibleTreap(const std::vector<S> &values, std::uint64_t seed = 0) : LazyReversibleTreap(seed) { assign(values); }
LazyReversibleTreap(const LazyReversibleTreap &) = default;
LazyReversibleTreap &operator=(const LazyReversibleTreap &) = default;
LazyReversibleTreap(LazyReversibleTreap &&other) : LazyReversibleTreap() { swap(other); }
LazyReversibleTreap &operator=(LazyReversibleTreap &&other) {
if (this != &other) { LazyReversibleTreap moved(std::move(other)); swap(moved); }
return *this;
}
void swap(LazyReversibleTreap &other) noexcept {
t.swap(other.t);
std::swap(rng, other.rng);
std::swap(root, other.root);
std::swap(free, other.free);
std::swap(lazy_applied, other.lazy_applied);
}
int size() const { return count(root); }
bool empty() const { return !root; }
void reserve(std::size_t n) { assert(n < (std::size_t(1) << 30)); t.reserve(n + 1); }
std::size_t memory_usage() const { return t.capacity() * sizeof(Node); }
void clear() { t.erase(t.begin() + 1, t.end()); root = free = 0; lazy_applied = false; }
void assign(const std::vector<S> &values) {
clear();
reserve(values.size());
std::vector<int> path;
for (const S &value : values) {
int x = make(value), last = 0;
while (!path.empty() && t[path.back()].priority <= t[x].priority) {
last = path.back(); path.pop_back(); pull(last);
}
t[x].left = last;
if (!path.empty()) t[path.back()].right = x;
path.push_back(x);
}
if (!path.empty()) root = path[0];
while (!path.empty()) { pull(path.back()); path.pop_back(); }
}
void insert(int p, S value) { bounds(p, p); root = insert_node(root, p, make(std::move(value))); }
S erase(int p) { bounds(p, p + 1); S value = e(); root = erase_node(root, p, value); return value; }
S get(int p) {
bounds(p, p + 1);
int x = root;
for (;;) {
push(x);
int left = count(t[x].left);
if (p == left) return t[x].value;
if (p < left) x = t[x].left;
else p -= left + 1, x = t[x].right;
}
}
void set(int p, S value) { bounds(p, p + 1); set_node(root, p, std::move(value)); }
S prod(int l, int r) { bounds(l, r); return l == r ? e() : lazy_applied ? fold_lazy(root, l, r) : fold(root, l, r); }
S all_prod() const { return t[root].product; }
void apply(int p, const F &f) { apply(p, p + 1, f); }
void apply(int l, int r, const F &f) { bounds(l, r); if (l != r) { lazy_applied = true; apply_node(root, l, r, f); } }
void reverse(int l, int r) { bounds(l, r); if (r - l > 1) root = reverse_node(root, l, r); }
void rotate(int l, int m, int r) {
bounds(l, m); bounds(m, r);
if (l == m || m == r) return;
auto [a, b] = split(root, l);
auto [c, d] = split(b, m - l);
auto [f, g] = split(d, r - m);
root = merge(a, merge(f, merge(c, g)));
}
void move(int l, int r, int p) {
bounds(l, r);
assert(0 <= p && p <= size() - (r - l));
if (l == r || l == p) return;
auto [a, b] = split(root, l);
auto [c, d] = split(b, r - l);
auto [f, g] = split(merge(a, d), p);
root = merge(f, merge(c, g));
}
std::vector<S> to_vector() { std::vector<S> values; values.reserve(size()); collect(root, values); return values; }
};
#if defined(__GNUC__) && !defined(__clang__) && (defined(__x86_64__) || defined(__i386__))
#pragma GCC pop_options
#endif
#line 1 "components/fast_io.hpp"
#line 5 "components/fast_io.hpp"
#include <array>
#include <bit>
#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 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 6 "test/lazy_reversible_treap_affine.test.cpp"
struct F { mint a, b; };
mint op(mint a, mint b) { return a + b; }
mint e() { return 0; }
mint mapping(F f, mint s, int n) { return f.a * s + f.b * n; }
F composition(F f, F g) { return {f.a * g.a, f.a * g.b + f.b}; }
F id() { return {1, 0}; }
int main() {
FastInput input;
FastOutput output;
int n = 0, q = 0;
input.read(n); input.read(q);
std::vector<mint> a(n);
for (auto &x : a) { unsigned value = 0; input.read(value); x = mint::raw(value); }
LazyReversibleTreap<mint, op, e, F, mapping, composition, id, true> tree(a);
tree.reserve(n + q);
while (q--) {
int type = 0, l = 0;
input.read(type); input.read(l);
if (type == 0) { unsigned x = 0; input.read(x); tree.insert(l, mint::raw(x)); }
else if (type == 1) tree.erase(l);
else {
int r = 0;
input.read(r);
if (type == 2) tree.reverse(l, r);
else if (type == 3) { unsigned b = 0, c = 0; input.read(b); input.read(c); tree.apply(l, r, {mint::raw(b), mint::raw(c)}); }
else { output.write(tree.prod(l, r).val()); output.write('\n'); }
}
}
}