結果
| 問題 | No.2303 Frog on Grid |
| ユーザー |
👑  emthrm
|
| 提出日時 | 2023-05-12 21:46:00 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 108 ms / 2,000 ms |
| コード長 | 8,717 bytes |
| コンパイル時間 | 3,295 ms |
| コンパイル使用メモリ | 263,192 KB |
| 実行使用メモリ | 14,616 KB |
| 最終ジャッジ日時 | 2024-11-28 17:51:10 |
| 合計ジャッジ時間 | 5,361 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 20 |
ソースコード
#include <bits/stdc++.h>using namespace std;#define FOR(i,m,n) for(int i=(m);i<(n);++i)#define REP(i,n) FOR(i,0,n)#define ALL(v) (v).begin(),(v).end()using ll = long long;constexpr int INF = 0x3f3f3f3f;constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;constexpr double EPS = 1e-8;constexpr int MOD = 998244353;// constexpr int MOD = 1000000007;constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1};constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1};constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1};template <typename T, typename U>inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; }template <typename T, typename U>inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; }struct IOSetup {IOSetup() {std::cin.tie(nullptr);std::ios_base::sync_with_stdio(false);std::cout << fixed << setprecision(20);}} iosetup;template <int M>struct MInt {unsigned int v;MInt() : v(0) {}MInt(const long long x) : v(x >= 0 ? x % M : x % M + M) {}static constexpr int get_mod() { return M; }static void set_mod(const int divisor) { assert(divisor == M); }static void init(const int x) {inv<true>(x);fact(x);fact_inv(x);}template <bool MEMOIZES = false>static MInt inv(const int n) {// assert(0 <= n && n < M && std::gcd(n, M) == 1);static std::vector<MInt> inverse{0, 1};const int prev = inverse.size();if (n < prev) return inverse[n];if constexpr (MEMOIZES) {// "n!" and "M" must be disjoint.inverse.resize(n + 1);for (int i = prev; i <= n; ++i) {inverse[i] = -inverse[M % i] * (M / i);}return inverse[n];}int u = 1, v = 0;for (unsigned int a = n, b = M; b;) {const unsigned int q = a / b;std::swap(a -= q * b, b);std::swap(u -= q * v, v);}return u;}static MInt fact(const int n) {static std::vector<MInt> factorial{1};const int prev = factorial.size();if (n >= prev) {factorial.resize(n + 1);for (int i = prev; i <= n; ++i) {factorial[i] = factorial[i - 1] * i;}}return factorial[n];}static MInt fact_inv(const int n) {static std::vector<MInt> f_inv{1};const int prev = f_inv.size();if (n >= prev) {f_inv.resize(n + 1);f_inv[n] = inv(fact(n).v);for (int i = n; i > prev; --i) {f_inv[i - 1] = f_inv[i] * i;}}return f_inv[n];}static MInt nCk(const int n, const int k) {if (n < 0 || n < k || k < 0) return 0;return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) :fact_inv(n - k) * fact_inv(k));}static MInt nPk(const int n, const int k) {return n < 0 || n < k || k < 0 ? 0 : fact(n) * fact_inv(n - k);}static MInt nHk(const int n, const int k) {return n < 0 || k < 0 ? 0 : (k == 0 ? 1 : nCk(n + k - 1, k));}static MInt large_nCk(long long n, const int k) {if (n < 0 || n < k || k < 0) return 0;inv<true>(k);MInt res = 1;for (int i = 1; i <= k; ++i) {res *= inv(i) * n--;}return res;}MInt pow(long long exponent) const {MInt res = 1, tmp = *this;for (; exponent > 0; exponent >>= 1) {if (exponent & 1) res *= tmp;tmp *= tmp;}return res;}MInt& operator+=(const MInt& x) {if (std::cmp_greater_equal(v += x.v, M)) v -= M;return *this;}MInt& operator-=(const MInt& x) {if (std::cmp_greater_equal(v += M - x.v, M)) v -= M;return *this;}MInt& operator*=(const MInt& x) {v = static_cast<unsigned long long>(v) * x.v % M;return *this;}MInt& operator/=(const MInt& x) { return *this *= inv(x.v); }auto operator<=>(const MInt& x) const = default;MInt& operator++() {if (std::cmp_equal(++v, M)) v = 0;return *this;}MInt operator++(int) {const MInt res = *this;++*this;return res;}MInt& operator--() {v = (v == 0 ? M - 1 : v - 1);return *this;}MInt operator--(int) {const MInt res = *this;--*this;return res;}MInt operator+() const { return *this; }MInt operator-() const { return MInt(v ? M - v : 0); }MInt operator+(const MInt& x) const { return MInt(*this) += x; }MInt operator-(const MInt& x) const { return MInt(*this) -= x; }MInt operator*(const MInt& x) const { return MInt(*this) *= x; }MInt operator/(const MInt& x) const { return MInt(*this) /= x; }friend std::ostream& operator<<(std::ostream& os, const MInt& x) {return os << x.v;}friend std::istream& operator>>(std::istream& is, MInt& x) {long long v;is >> v;x = MInt(v);return is;}};using ModInt = MInt<MOD>;template <int T>struct NumberTheoreticTransform {using ModInt = MInt<T>;NumberTheoreticTransform() {for (int i = 0; i < 23; ++i) {if (primes[i][0] == ModInt::get_mod()) [[unlikely]] {n_max = 1 << primes[i][2];root = ModInt(primes[i][1]).pow((primes[i][0] - 1) >> primes[i][2]);return;}}assert(false);}template <typename U>std::vector<ModInt> dft(const std::vector<U>& a) {std::vector<ModInt> b(std::bit_ceil(a.size()), 0);std::copy(a.begin(), a.end(), b.begin());calc(&b);return b;}void idft(std::vector<ModInt>* a) {assert(std::has_single_bit(a->size()));calc(a);std::reverse(std::next(a->begin()), a->end());const int n = a->size();const ModInt inv_n = ModInt::inv(n);for (int i = 0; i < n; ++i) {(*a)[i] *= inv_n;}}template <typename U>std::vector<ModInt> convolution(const std::vector<U>& a,const std::vector<U>& b) {const int a_size = a.size(), b_size = b.size();const int c_size = a_size + b_size - 1;const int n = std::bit_ceil(static_cast<unsigned int>(c_size));std::vector<ModInt> c(n, 0), d(n, 0);std::copy(a.begin(), a.end(), c.begin());calc(&c);std::copy(b.begin(), b.end(), d.begin());calc(&d);for (int i = 0; i < n; ++i) {c[i] *= d[i];}idft(&c);c.resize(c_size);return c;}private:const int primes[23][3]{{16957441, 329, 14},{17006593, 26, 15},{19529729, 770, 17},{167772161, 3, 25},{469762049, 3, 26},{645922817, 3, 23},{897581057, 3, 23},{924844033, 5, 21},{935329793, 3, 22},{943718401, 7, 22},{950009857, 7, 21},{962592769, 7, 21},{975175681, 17, 21},{976224257, 3, 20},{985661441, 3, 22},{998244353, 3, 23},{1004535809, 3, 21},{1007681537, 3, 20},{1012924417, 5, 21},{1045430273, 3, 20},{1051721729, 6, 20},{1053818881, 7, 20},{1224736769, 3, 24}};int n_max;ModInt root;std::vector<int> butterfly{0};std::vector<std::vector<ModInt>> omega{{1}};void calc(std::vector<ModInt>* a) {const int n = a->size(), prev_n = butterfly.size();if (n > prev_n) {assert(n <= n_max);butterfly.resize(n);const int prev_lg = omega.size(), lg = std::countr_zero(a->size());for (int i = 1; i < prev_n; ++i) {butterfly[i] <<= lg - prev_lg;}for (int i = prev_n; i < n; ++i) {butterfly[i] = (butterfly[i >> 1] >> 1) | ((i & 1) << (lg - 1));}omega.resize(lg);for (int i = prev_lg; i < lg; ++i) {omega[i].resize(1 << i);const ModInt tmp = root.pow((ModInt::get_mod() - 1) >> (i + 1));for (int j = 0; j < (1 << (i - 1)); ++j) {omega[i][j << 1] = omega[i - 1][j];omega[i][(j << 1) + 1] = omega[i - 1][j] * tmp;}}}const int shift =std::countr_zero(butterfly.size()) - std::countr_zero(a->size());for (int i = 0; i < n; ++i) {const int j = butterfly[i] >> shift;if (i < j) std::swap((*a)[i], (*a)[j]);}for (int block = 1, den = 0; block < n; block <<= 1, ++den) {for (int i = 0; i < n; i += (block << 1)) {for (int j = 0; j < block; ++j) {const ModInt tmp = (*a)[i + j + block] * omega[den][j];(*a)[i + j + block] = (*a)[i + j] - tmp;(*a)[i + j] += tmp;}}}}};int main() {int h, w; cin >> h >> w;vector<ModInt> y(h + 1, 0), x(w + 1, 0);FOR(i, (h + 1) / 2, h + 1) y[i] = ModInt::nCk(i, h - i) * ModInt::fact_inv(i);FOR(i, (w + 1) / 2, w + 1) x[i] = ModInt::nCk(i, w - i) * ModInt::fact_inv(i);const vector<ModInt> c = NumberTheoreticTransform<MOD>().convolution(y, x);ModInt ans = 0;REP(i, c.size()) ans += c[i] * ModInt::fact(i);cout << ans << '\n';return 0;}