結果
問題 | No.1431 東大文系数学2020第2問改 |
ユーザー |
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提出日時 | 2024-11-25 16:10:29 |
言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 643 ms / 5,000 ms |
コード長 | 13,232 bytes |
コンパイル時間 | 1,548 ms |
コンパイル使用メモリ | 138,328 KB |
実行使用メモリ | 120,556 KB |
最終ジャッジ日時 | 2024-11-25 16:10:47 |
合計ジャッジ時間 | 16,517 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge1 |
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ファイルパターン | 結果 |
---|---|
other | AC * 28 |
ソースコード
#include<iostream>#include<string>#include<vector>#include<algorithm>#include<numeric>#include<cmath>#include<utility>#include<tuple>#include<array>#include<cstdint>#include<cstdio>#include<iomanip>#include<map>#include<set>#include<unordered_map>#include<unordered_set>#include<queue>#include<stack>#include<deque>#include<bitset>#include<cctype>#include<chrono>#include<random>#include<cassert>#include<cstddef>#include<iterator>#include<string_view>#include<type_traits>#include<functional>#ifdef LOCAL# include "debug_print.hpp"# define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)#else# define debug(...) (static_cast<void>(0))#endifusing namespace std;template<typename T, typename U>ostream &operator<<(ostream &os, const pair<T, U> &p) {os << p.first << " " << p.second;return os;}template<typename T, typename U>istream &operator>>(istream &is, pair<T, U> &p) {is >> p.first >> p.second;return is;}template<typename T>ostream &operator<<(ostream &os, const vector<T> &v) {int s = (int)v.size();for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];return os;}template<typename T>istream &operator>>(istream &is, vector<T> &v) {for (auto &x : v) is >> x;return is;}void in() {}template<typename T, class... U>void in(T &t, U &...u) {cin >> t;in(u...);}void out() { cout << "\n"; }template<typename T, class... U, char sep = ' '>void out(const T &t, const U &...u) {cout << t;if (sizeof...(u)) cout << sep;out(u...);}void outr() {}template<typename T, class... U, char sep = ' '>void outr(const T &t, const U &...u) {cout << t;outr(u...);}using ll = long long;using D = double;using LD = long double;using P = pair<ll, ll>;using u8 = uint8_t;using u16 = uint16_t;using u32 = uint32_t;using u64 = uint64_t;using i128 = __int128;using u128 = unsigned __int128;using vi = vector<ll>;template <class T> using vc = vector<T>;template <class T> using vvc = vector<vc<T>>;template <class T> using vvvc = vector<vvc<T>>;template <class T> using vvvvc = vector<vvvc<T>>;template <class T> using vvvvvc = vector<vvvvc<T>>;#define vv(type, name, h, ...) \vector<vector<type>> name(h, vector<type>(__VA_ARGS__))#define vvv(type, name, h, w, ...) \vector<vector<vector<type>>> name( \h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))#define vvvv(type, name, a, b, c, ...) \vector<vector<vector<vector<type>>>> name( \a, vector<vector<vector<type>>>( \b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))template<typename T> using PQ = priority_queue<T,vector<T>>;template<typename T> using minPQ = priority_queue<T, vector<T>, greater<T>>;#define rep1(a) for(ll i = 0; i < a; i++)#define rep2(i, a) for(ll i = 0; i < a; i++)#define rep3(i, a, b) for(ll i = a; i < b; i++)#define rep4(i, a, b, c) for(ll i = a; i < b; i += c)#define overload4(a, b, c, d, e, ...) e#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)#define rrep1(a) for(ll i = (a)-1; i >= 0; i--)#define rrep2(i, a) for(ll i = (a)-1; i >= 0; i--)#define rrep3(i, a, b) for(ll i = (b)-1; i >= a; i--)#define rrep4(i, a, b, c) for(ll i = (b)-1; i >= a; i -= c)#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)#define for_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))#define ALL(v) v.begin(), v.end()#define RALL(v) v.rbegin(), v.rend()#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() )#define SZ(v) ll(v.size())#define MIN(v) *min_element(ALL(v))#define MAX(v) *max_element(ALL(v))#define LB(c, x) distance((c).begin(), lower_bound(ALL(c), (x)))#define UB(c, x) distance((c).begin(), upper_bound(ALL(c), (x)))template <typename T, typename U>T SUM(const vector<U> &v) {T res = 0;for(auto &&a : v) res += a;return res;}template <typename T>vector<pair<T,int>> RLE(const vector<T> &v) {if (v.empty()) return {};T cur = v.front();int cnt = 1;vector<pair<T,int>> res;for (int i = 1; i < (int)v.size(); i++) {if (cur == v[i]) cnt++;else {res.emplace_back(cur, cnt);cnt = 1; cur = v[i];}}res.emplace_back(cur, cnt);return res;}template<class T, class S>inline bool chmax(T &a, const S &b) { return (a < b ? a = b, true : false); }template<class T, class S>inline bool chmin(T &a, const S &b) { return (a > b ? a = b, true : false); }void YESNO(bool flag) { out(flag ? "YES" : "NO"); }void yesno(bool flag) { out(flag ? "Yes" : "No"); }int popcnt(int x) { return __builtin_popcount(x); }int popcnt(u32 x) { return __builtin_popcount(x); }int popcnt(ll x) { return __builtin_popcountll(x); }int popcnt(u64 x) { return __builtin_popcountll(x); }int popcnt_sgn(int x) { return (__builtin_parity(x) & 1 ? -1 : 1); }int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }int popcnt_sgn(ll x) { return (__builtin_parity(x) & 1 ? -1 : 1); }int popcnt_sgn(u64 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }int highbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }int highbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }int highbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }int highbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }template <typename T>T get_bit(T x, int k) { return x >> k & 1; }template <typename T>T set_bit(T x, int k) { return x | T(1) << k; }template <typename T>T reset_bit(T x, int k) { return x & ~(T(1) << k); }template <typename T>T flip_bit(T x, int k) { return x ^ T(1) << k; }template <typename T>T popf(deque<T> &que) { T a = que.front(); que.pop_front(); return a; }template <typename T>T popb(deque<T> &que) { T a = que.back(); que.pop_back(); return a; }template <typename T>T pop(queue<T> &que) { T a = que.front(); que.pop(); return a; }template <typename T>T pop(PQ<T> &que) { T a = que.top(); que.pop(); return a; }template <typename T>T pop(minPQ<T> &que) { T a = que.top(); que.pop(); return a; }template <typename F>ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {if (check_ok) assert(check(ok));while (abs(ok - ng) > 1) {ll mid = (ok + ng) / 2;(check(mid) ? ok : ng) = mid;}return ok;}template <typename F>ll binary_search_real(F check, double ok, double ng, int iter = 60) {for (int _ = 0; _ < iter; _++) {double mid = (ok + ng) / 2;(check(mid) ? ok : ng) = mid;}return (ok + ng) / 2;}// max x s.t. b*x <= all div_floor(ll a, ll b) {assert(b != 0);if (b < 0) a = -a, b = -b;return a / b - (a % b < 0);}// max x s.t. b*x < all div_under(ll a, ll b) {assert(b != 0);if (b < 0) a = -a, b = -b;return a / b - (a % b <= 0);}// min x s.t. b*x >= all div_ceil(ll a, ll b) {assert(b != 0);if (b < 0) a = -a, b = -b;return a / b + (a % b > 0);}// min x s.t. b*x > all div_over(ll a, ll b) {assert(b != 0);if (b < 0) a = -a, b = -b;return a / b + (a % b >= 0);}// x = a mod b (b > 0), 0 <= x < bll modulo(ll a, ll b) {assert(b > 0);ll c = a % b;return c < 0 ? c + b : c;}// (q,r) s.t. a = b*q + r, 0 <= r < b (b > 0)// div_floor(a,b), modulo(a,b)pair<ll,ll> divmod(ll a, ll b) {ll q = div_floor(a,b);return {q, a - b*q};}template <uint32_t mod>struct LazyMontgomeryModInt {using mint = LazyMontgomeryModInt;using i32 = int32_t;using u32 = uint32_t;using u64 = uint64_t;static constexpr u32 get_r() {u32 ret = mod;for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;return ret;}static constexpr u32 r = get_r();static constexpr u32 n2 = -u64(mod) % mod;static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");static_assert(r * mod == 1, "this code has bugs.");u32 a;constexpr LazyMontgomeryModInt() : a(0) {}constexpr LazyMontgomeryModInt(const int64_t &b): a(reduce(u64(b % mod + mod) * n2)){};static constexpr u32 reduce(const u64 &b) {return (b + u64(u32(b) * u32(-r)) * mod) >> 32;}constexpr mint &operator+=(const mint &b) {if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;return *this;}constexpr mint &operator-=(const mint &b) {if (i32(a -= b.a) < 0) a += 2 * mod;return *this;}constexpr mint &operator*=(const mint &b) {a = reduce(u64(a) * b.a);return *this;}constexpr mint &operator/=(const mint &b) {*this *= b.inverse();return *this;}constexpr mint operator+(const mint &b) const { return mint(*this) += b; }constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }constexpr bool operator==(const mint &b) const {return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);}constexpr bool operator!=(const mint &b) const {return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);}constexpr mint operator-() const { return mint() - mint(*this); }constexpr mint operator+() const { return mint(*this); }constexpr mint pow(u64 n) const {mint ret(1), mul(*this);while (n > 0) {if (n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}constexpr mint inverse() const {int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;while (y > 0) {t = x / y;x -= t * y, u -= t * v;tmp = x, x = y, y = tmp;tmp = u, u = v, v = tmp;}return mint{u};}friend ostream &operator<<(ostream &os, const mint &b) {return os << b.get();}friend istream &operator>>(istream &is, mint &b) {int64_t t;is >> t;b = LazyMontgomeryModInt<mod>(t);return (is);}constexpr u32 get() const {u32 ret = reduce(a);return ret >= mod ? ret - mod : ret;}static constexpr u32 get_mod() { return mod; }};template<typename T> struct Binomial {vector<T> fact_, inv_, finv_;constexpr Binomial() {}constexpr Binomial(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) {init(n);}constexpr void init(int n) noexcept {constexpr int mod = T::get_mod();fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);for(int i = 2; i < n; i++){fact_[i] = fact_[i-1] * i;inv_[i] = -inv_[mod%i] * (mod/i);finv_[i] = finv_[i-1] * inv_[i];}}constexpr T com(int n, int k) const noexcept {if (n < k || n < 0 || k < 0) return 0;return fact_[n] * finv_[k] * finv_[n-k];}constexpr T perm(int n, int k) const noexcept {if (n < k || n < 0 || k < 0) return 0;return fact_[n] * finv_[n-k];}constexpr T fact(int n) const noexcept {if (n < 0) return 0;return fact_[n];}constexpr T inv(int n) const noexcept {if (n < 0) return 0;return inv_[n];}constexpr T finv(int n) const noexcept {if (n < 0) return 0;return finv_[n];}constexpr T com_naive(int n, int k) const noexcept {if (n < 0 || k < 0 || n < k) return 0;T res = T(1);k = min(k, n-k);for (int i = 1; i <= k; i++)res *= (n--) * inv(i);return res;}template <typename I>constexpr T multi(const vector<I> &v) const noexcept {static_assert(is_integral<I>::value);I n = 0;for (auto& x : v) {if (x < 0) return 0;n += x;}T res = fact(n);for (auto &x : v) res *= finv(x);return res;}// [x^k] (1-x)^{-n} = com(n+k-1, k)constexpr T neg(int n, int k) const noexcept {if (n < 0 || k < 0) return 0;return k == 0 ? 1 : com(n+k-1, k);}};const int mod = 998244353;//const int mod = 1000000007;using mint = LazyMontgomeryModInt<mod>;Binomial<mint> bc(10000000);int main() {ios_base::sync_with_stdio(false);cin.tie(nullptr);int n,m,k; in(n,m,k);vector<mint> f(n*2+1);rep(i,n*2+1){rep(a,i+1){int b = i-a;f[i] += bc.com(n,a) * bc.com(n,b) * bc.com((n-a)*(n-b),m);}}vector<mint> a(n*2+1), b(n*2+1); b[k] = 1;rep(i,n*2+1) rep(j,i+1) a[i] += b[j] * bc.com(i,j) * ((i-j)%2 ? -1:1);mint ans = 0;rep(i,n*2+1) ans += f[i]*a[i];out(ans);}