結果
| 問題 |
No.1696 Nonnil
|
| コンテスト | |
| ユーザー |
 KoD
|
| 提出日時 | 2021-10-01 23:25:24 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 227 ms / 3,500 ms |
| コード長 | 11,125 bytes |
| コンパイル時間 | 3,120 ms |
| コンパイル使用メモリ | 264,248 KB |
| 実行使用メモリ | 21,248 KB |
| 最終ジャッジ日時 | 2024-07-19 16:17:08 |
| 合計ジャッジ時間 | 8,408 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 39 |
ソースコード
#include <bits/stdc++.h>
using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using isize = std::ptrdiff_t;
using usize = std::size_t;
class rep {
struct Iter {
usize itr;
constexpr Iter(const usize pos) noexcept : itr(pos) {}
constexpr void operator++() noexcept { ++itr; }
constexpr bool operator!=(const Iter& other) const noexcept { return itr != other.itr; }
constexpr usize operator*() const noexcept { return itr; }
};
const Iter first, last;
public:
explicit constexpr rep(const usize first, const usize last) noexcept : first(first), last(std::max(first, last)) {}
constexpr Iter begin() const noexcept { return first; }
constexpr Iter end() const noexcept { return last; }
};
template <class T> constexpr T totient(T x) {
T ret = x;
for (T i = 2; i * i <= x; ++i) {
if (x % i == 0) {
ret /= i;
ret *= i - 1;
while (x % i == 0) x /= i;
}
}
if (x > 1) {
ret /= x;
ret *= x - 1;
}
return ret;
}
template <class T> constexpr T rem_euclid(T value, const T& mod) { return (value %= mod) >= 0 ? value : value + mod; }
template <u32 MOD, std::enable_if_t<((u32)1 <= MOD and MOD <= ((u32)1 << 31))>* = nullptr> class StaticModint {
using Mint = StaticModint;
static inline constexpr u32 PHI = totient(MOD);
u32 v;
public:
static constexpr u32 mod() noexcept { return MOD; }
template <class T, std::enable_if_t<std::is_signed_v<T> and std::is_integral_v<T>>* = nullptr>
static constexpr T normalize(const T x) noexcept {
return rem_euclid<std::common_type_t<T, i64>>(x, MOD);
}
template <class T, std::enable_if_t<std::is_unsigned_v<T> and std::is_integral_v<T>>* = nullptr>
static constexpr T normalize(const T x) noexcept {
return x % MOD;
}
constexpr StaticModint() noexcept : v(0) {}
template <class T> constexpr StaticModint(const T x) noexcept : v(normalize(x)) {}
template <class T> static constexpr Mint raw(const T x) noexcept {
Mint ret;
ret.v = x;
return ret;
}
constexpr u32 get() const noexcept { return v; }
constexpr Mint neg() const noexcept { return raw(v == 0 ? 0 : MOD - v); }
constexpr Mint inv() const noexcept { return pow(PHI - 1); }
constexpr Mint pow(u64 exp) const noexcept {
Mint ret(1), mult(*this);
for (; exp > 0; exp >>= 1) {
if (exp & 1) ret *= mult;
mult *= mult;
}
return ret;
}
constexpr Mint operator-() const noexcept { return neg(); }
constexpr Mint operator~() const noexcept { return inv(); }
constexpr Mint operator+(const Mint& rhs) const noexcept { return Mint(*this) += rhs; }
constexpr Mint& operator+=(const Mint& rhs) noexcept {
if ((v += rhs.v) >= MOD) v -= MOD;
return *this;
}
constexpr Mint operator-(const Mint& rhs) const noexcept { return Mint(*this) -= rhs; }
constexpr Mint& operator-=(const Mint& rhs) noexcept {
if (v < rhs.v) v += MOD;
v -= rhs.v;
return *this;
}
constexpr Mint operator*(const Mint& rhs) const noexcept { return Mint(*this) *= rhs; }
constexpr Mint& operator*=(const Mint& rhs) noexcept {
v = (u64)v * rhs.v % MOD;
return *this;
}
constexpr Mint operator/(const Mint& rhs) const noexcept { return Mint(*this) /= rhs; }
constexpr Mint& operator/=(const Mint& rhs) noexcept { return *this *= rhs.inv(); }
constexpr bool operator==(const Mint& rhs) const noexcept { return v == rhs.v; }
constexpr bool operator!=(const Mint& rhs) const noexcept { return v != rhs.v; }
friend std::ostream& operator<<(std::ostream& stream, const Mint& rhs) { return stream << rhs.v; }
};
using Modint1000000007 = StaticModint<1000000007>;
using Modint998244353 = StaticModint<998244353>;
__attribute__((target("avx2"))) constexpr u64 ceil_log2(const u64 x) {
u64 e = 0;
while (((u64)1 << e) < x) ++e;
return e;
}
template <class F> class AutoReallocation {
using R = typename decltype(std::declval<F>()((usize)0))::value_type;
F func;
mutable std::vector<R> data;
public:
explicit AutoReallocation(F&& f) : func(std::forward<F>(f)), data() {}
void reserve(const usize size) const {
if (data.size() < size) data = func(((usize)1 << ceil_log2(size)));
}
R operator[](const usize i) const {
reserve(i + 1);
return data[i];
}
};
template <class F> decltype(auto) auto_realloc(F&& f) {
using G = std::decay_t<F>;
return AutoReallocation<G>(std::forward<G>(f));
}
template <class M> struct ModintUtil {
static inline const auto fact = auto_realloc([](const usize n) {
std::vector<M> ret(n);
ret[0] = M(1);
for (const usize i : rep(1, n)) {
ret[i] = ret[i - 1] * M(i);
}
return ret;
});
static inline const auto inv = auto_realloc([](const usize n) {
std::vector<M> ret(n);
if (n == 1) return ret;
ret[1] = M(1);
for (const usize i : rep(2, n)) {
ret[i] = -M(M::mod() / i) * ret[M::mod() % i];
}
return ret;
});
static inline const auto inv_fact = auto_realloc([](const usize n) {
std::vector<M> ret(n);
ret[0] = M(1);
for (const usize i : rep(1, n)) {
ret[i] = ret[i - 1] * inv[i];
}
return ret;
});
static M binom(const usize n, const usize k) {
assert(k <= n);
return fact[n] * inv_fact[n - k] * inv_fact[k];
}
static M factpow(const usize n, const usize k) {
assert(k <= n);
return fact[n] * inv_fact[n - k];
}
static M homo(const usize n, const usize k) {
if (n == 0 and k == 0) return M(1);
return binom(n + k - 1, k);
}
};
class revrep {
struct Iter {
usize itr;
constexpr Iter(const usize pos) noexcept : itr(pos) {}
constexpr void operator++() noexcept { --itr; }
constexpr bool operator!=(const Iter& other) const noexcept { return itr != other.itr; }
constexpr usize operator*() const noexcept { return itr; }
};
const Iter first, last;
public:
explicit constexpr revrep(const usize first, const usize last) noexcept
: first(last - 1), last(std::min(first, last) - 1) {}
constexpr Iter begin() const noexcept { return first; }
constexpr Iter end() const noexcept { return last; }
};
template <class M> class SegmentTree {
using T = typename M::Type;
usize internal_size, seg_size;
std::vector<T> data;
void fetch(const usize k) { data[k] = M::operation(data[2 * k], data[2 * k + 1]); }
public:
explicit SegmentTree(const usize size = 0, const T& value = M::identity())
: SegmentTree(std::vector<T>(size, value)) {}
explicit SegmentTree(const std::vector<T>& vec) : internal_size(vec.size()) {
seg_size = 1 << ceil_log2(internal_size);
data = std::vector<T>(2 * seg_size, M::identity());
for (const usize i : rep(0, internal_size)) data[seg_size + i] = vec[i];
for (const usize i : revrep(1, seg_size)) fetch(i);
}
usize size() const { return internal_size; }
void assign(usize i, const T& value) {
assert(i < internal_size);
i += seg_size;
data[i] = value;
while (i > 1) {
i >>= 1;
fetch(i);
}
}
T fold() const { return data[1]; }
T fold(usize l, usize r) const {
assert(l <= r and r <= internal_size);
l += seg_size;
r += seg_size;
T ret_l = M::identity(), ret_r = M::identity();
while (l < r) {
if (l & 1) ret_l = M::operation(ret_l, data[l++]);
if (r & 1) ret_r = M::operation(data[--r], ret_r);
l >>= 1;
r >>= 1;
}
return M::operation(ret_l, ret_r);
}
template <class F> usize max_right(usize l, const F& f) const {
assert(l <= internal_size);
assert(f(M::identity()));
if (l == internal_size) return internal_size;
l += seg_size;
T sum = M::identity();
do {
while (!(l & 1)) l >>= 1;
if (!f(M::operation(sum, data[l]))) {
while (l < seg_size) {
l = 2 * l;
if (f(M::operation(sum, data[l]))) sum = M::operation(sum, data[l++]);
}
return l - seg_size;
}
sum = M::operation(sum, data[l++]);
} while ((l & -l) != l);
return internal_size;
}
template <class F> usize min_left(usize r, const F& f) const {
assert(r <= internal_size);
assert(f(M::identity()));
if (r == 0) return 0;
r += seg_size;
T sum = M::identity();
do {
r -= 1;
while (r > 1 and (r & 1)) r >>= 1;
if (!f(M::operation(data[r], sum))) {
while (r < seg_size) {
r = 2 * r + 1;
if (f(M::operation(data[r], sum))) sum = M::operation(data[r--], sum);
}
return r + 1 - seg_size;
}
sum = M::operation(data[r], sum);
} while ((r & -r) != r);
return 0;
}
};
#include <optional>
template <class S> struct OptionalMonoid {
using Type = std::optional<typename S::Type>;
static constexpr Type identity() { return std::nullopt; }
static constexpr Type operation(const Type& l, const Type& r) {
if (!l) return r;
if (!r) return l;
return Type(std::in_place, S::operation(*l, *r));
}
};
template <class T> bool setmax(T& lhs, const T& rhs) {
if (lhs < rhs) {
lhs = rhs;
return true;
}
return false;
}
template <class T> using Vec = std::vector<T>;
using Fp = Modint998244353;
using Util = ModintUtil<Fp>;
struct Add {
using Type = std::valarray<Fp>;
static Type operation(const Type& l, const Type& r) { return l + r; }
};
using Monoid = OptionalMonoid<Add>;
void main_() {
usize N, K, M;
std::cin >> N >> K >> M;
Vec<usize> max(K + 1);
while (M--) {
usize l, r;
std::cin >> l >> r;
setmax(max[r], l);
}
SegmentTree<Monoid> seg(K + 1);
{
std::valarray<Fp> tmp(K + 1);
tmp[0] = 1;
seg.assign(0, tmp);
}
usize left = 0;
for (const auto r : rep(1, K + 1)) {
seg.assign(r, seg.fold(left, r)->cshift(-1));
setmax(left, max[r]);
}
const auto ans = *seg.fold(left, K + 1);
Fp sum;
for (const auto k : rep(1, std::min(N, K) + 1)) {
Fp coeff;
for (const auto i : rep(0, k + 1)) {
coeff += Fp(i % 2 == 0 ? 1 : -1) * Util::binom(k, k - i) * Fp(k - i).pow(N);
}
sum += coeff * ans[k];
}
std::cout << sum << '\n';
}
int main() {
std::ios_base::sync_with_stdio(false);
std::cin.tie(nullptr);
main_();
return 0;
}