結果

問題 No.2303 Frog on Grid
ユーザー Forested
提出日時 2023-05-12 21:57:21
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 57 ms / 2,000 ms
コード長 15,496 bytes
コンパイル時間 1,268 ms
コンパイル使用メモリ 135,096 KB
最終ジャッジ日時 2025-02-12 22:41:08
ジャッジサーバーID
（参考情報） 		judge2 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 20
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ソースコード

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プレゼンテーションモードにする

#ifndef LOCAL
#define FAST_IO
#endif
// ============
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER(i, n) for (i32 i = (i32)(n) - 1; i >= 0; --i)
#define ALL(x) begin(x), end(x)
using namespace std;
using u32 = unsigned int;
using u64 = unsigned long long;
using i32 = signed int;
using i64 = signed long long;
using f64 = double;
using f80 = long double;
template <typename T>
using Vec = vector<T>;
template <typename T>
bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
Vec<tuple<i32, i32, T>> runlength(const Vec<T> &a) {
    if (a.empty()) {
        return Vec<tuple<i32, i32, T>>();
    }
    Vec<tuple<i32, i32, T>> ret;
    i32 prv = 0;
    REP(i, 1, a.size()) {
        if (a[i - 1] != a[i]) {
            ret.emplace_back(prv, i, a[i - 1]);
            prv = i;
        }
    }
    ret.emplace_back(prv, (i32)a.size(), a.back());
    return ret;
}
#ifdef INT128
using u128 = __uint128_t;
using i128 = __int128_t;
istream &operator>>(istream &is, i128 &x) {
    i64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, i128 x) {
    os << (i64)x;
    return os;
}
istream &operator>>(istream &is, u128 &x) {
    u64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, u128 x) {
    os << (u64)x;
    return os;
}
#endif
[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
    SetUpIO() {
#ifdef FAST_IO
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
#endif
        cout << fixed << setprecision(15);
    }
} set_up_io;
// ============
#ifdef DEBUGF
#else
#define DBG(x) (void)0
#endif
// ============
#include <cassert>
#include <iostream>
#include <type_traits>
// ============
constexpr bool is_prime(unsigned n) {
    if (n == 0 || n == 1) {
        return false;
    }
    for (unsigned i = 2; i * i <= n; ++i) {
        if (n % i == 0) {
            return false;
        }
    }
    return true;
}
constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {
    unsigned ret = 1, self = x;
    while (y != 0) {
        if (y & 1) {
            ret = (unsigned) ((unsigned long long) ret * self % mod);
        }
        self = (unsigned) ((unsigned long long) self * self % mod);
        y /= 2;
    }
    return ret;
}
template <unsigned mod>
constexpr unsigned primitive_root() {
    static_assert(is_prime(mod), "`mod` must be a prime number.");
    if (mod == 2) {
        return 1;
    }
    unsigned primes[32] = {};
    int it = 0;
    {
        unsigned m = mod - 1;
        for (unsigned i = 2; i * i <= m; ++i) {
            if (m % i == 0) {
                primes[it++] = i;
                while (m % i == 0) {
                    m /= i;
                }
            }
        }
        if (m != 1) {
            primes[it++] = m;
        }
    }
    for (unsigned i = 2; i < mod; ++i) {
        bool ok = true;
        for (int j = 0; j < it; ++j) {
            if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {
                ok = false;
                break;
            }
        }
        if (ok)
            return i;
    }
    return 0;
}
// y >= 1
template <typename T>
constexpr T safe_mod(T x, T y) {
    x %= y;
    if (x < 0) {
        x += y;
    }
    return x;
}
// y != 0
template <typename T>
constexpr T floor_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return x / y;
    } else {
        return -((-x + y - 1) / y);
    }
}
// y != 0
template <typename T>
constexpr T ceil_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return (x + y - 1) / y;
    } else {
        return -(-x / y);
    }
}
// ============
template <unsigned mod>
class ModInt {
    static_assert(mod != 0, "`mod` must not be equal to 0.");
    static_assert(
        mod < (1u << 31),
        "`mod` must be less than (1u << 31) = 2147483648.");
    unsigned val;
public:
    static constexpr unsigned get_mod() {
        return mod;
    }
    
    constexpr ModInt() : val(0) {}
    template <typename T, std::enable_if_t<std::is_signed_v<T>> * = nullptr>
    constexpr ModInt(T x) : val((unsigned) ((long long) x % (long long) mod + (x < 0 ? mod : 0))) {}
    template <typename T, std::enable_if_t<std::is_unsigned_v<T>> * = nullptr>
    constexpr ModInt(T x) : val((unsigned) (x % mod)) {}
    static constexpr ModInt raw(unsigned x) {
        ModInt<mod> ret;
        ret.val = x;
        return ret;
    }
    constexpr unsigned get_val() const {
        return val;
    }
    constexpr ModInt operator+() const {
        return *this;
    }
    constexpr ModInt operator-() const {
        return ModInt<mod>(0u) - *this;
    }
    constexpr ModInt &operator+=(const ModInt &rhs) {
        val += rhs.val;
        if (val >= mod)
            val -= mod;
        return *this;
    }
    constexpr ModInt &operator-=(const ModInt &rhs) {
        if (val < rhs.val)
            val += mod;
        val -= rhs.val;
        return *this;
    }
    constexpr ModInt &operator*=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.val % mod;
        return *this;
    }
    constexpr ModInt &operator/=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.inv().val % mod;
        return *this;
    }
    friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) += rhs;
    }
    friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) -= rhs;
    }
    friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) *= rhs;
    }
    friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) /= rhs;
    }
    constexpr ModInt pow(unsigned long long x) const {
        ModInt<mod> ret = ModInt<mod>::raw(1);
        ModInt<mod> self = *this;
        while (x != 0) {
            if (x & 1)
                ret *= self;
            self *= self;
            x >>= 1;
        }
        return ret;
    }
    constexpr ModInt inv() const {
        static_assert(is_prime(mod), "`mod` must be a prime number.");
        assert(val != 0);
        return this->pow(mod - 2);
    }
    friend std::istream &operator>>(std::istream &is, ModInt<mod> &x) {
        long long val;
        is >> val;
        x.val = val % mod + (val < 0 ? mod : 0);
        return is;
    }
    friend std::ostream &operator<<(std::ostream &os, const ModInt<mod> &x) {
        os << x.val;
        return os;
    }
    friend bool operator==(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val == rhs.val;
    }
    
    friend bool operator!=(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val != rhs.val;
    }
};
[[maybe_unused]] constexpr unsigned mod998244353 = 998244353;
[[maybe_unused]] constexpr unsigned mod1000000007 = 1000000007;
// ============
// ============
#include <vector>
#include <cassert>
template <typename T>
class FactorialTable {
    std::vector<T> fac;
    std::vector<T> ifac;
    
public:
    FactorialTable() : fac(1, T(1)), ifac(1, T(1)) {}
    
    FactorialTable(int n) : fac(n + 1), ifac(n + 1) {
        assert(n >= 0);
        fac[0] = T(1);
        for (int i = 1; i <= n; ++i) {
            fac[i] = fac[i - 1] * T(i);
        }
        ifac[n] = T(1) / T(fac[n]);
        for (int i = n; i > 0; --i) {
            ifac[i - 1] = ifac[i] * T(i);
        }
    }
    
    void resize(int n) {
        int old = n_max();
        if (n <= old) {
            return;
        }
        fac.resize(n + 1);
        for (int i = old + 1; i <= n; ++i) {
            fac[i] = fac[i - 1] * T(i);
        }
        ifac.resize(n + 1);
        ifac[n] = T(1) / T(fac[n]);
        for (int i = n; i > old; --i) {
            ifac[i - 1] = ifac[i] * T(i);
        }
    }
    
    inline int n_max() const {
        return (int) fac.size() - 1;
    }
    
    inline T fact(int n) const {
        assert(n >= 0 && n <= n_max());
        return fac[n];
    }
    
    inline T inv_fact(int n) const {
        assert(n >= 0 && n <= n_max());
        return ifac[n];
    }
    
    inline T choose(int n, int k) const {
        assert(k <= n_max() && n <= n_max());
        if (k > n || k < 0) {
            return T(0);
        }
        return fac[n] * ifac[k] * ifac[n - k];
    }
    
    inline T multi_choose(int n, int k) const {
        assert(n >= 1 && k >= 0 && k + n - 1 <= n_max());
        return choose(k + n - 1, k);
    }
    
    inline T n_terms_sum_k(int n, int k) const {
        assert(n >= 0);
        if (k < 0) {
            return T(0);
        }
        if (n == 0) {
            return k == 0 ? T(1) : T(0);
        }
        return choose(n + k - 1, n - 1);
    }
};
// ============
// ============
#include <array>
#include <vector>
// ============
// ============
// ============
template <typename T, typename U>
bool ith_bit(T n, U i) {
    return (n & ((T) 1 << i)) != 0;
}
int popcount(int x) {
    return __builtin_popcount(x);
}
unsigned popcount(unsigned x) {
    return __builtin_popcount(x);
}
long long popcount(long long x) {
    return __builtin_popcountll(x);
}
unsigned long long popcount(unsigned long long x) {
    return __builtin_popcountll(x);
}
// x must not be 0
int clz(int x) {
    return __builtin_clz(x);
}
unsigned clz(unsigned x) {
    return __builtin_clz(x);
}
long long clz(long long x) {
    return __builtin_clzll(x);
}
unsigned long long clz(unsigned long long x) {
    return __builtin_clzll(x);
}
// x must not be 0
int ctz(int x) {
    return __builtin_ctz(x);
}
unsigned ctz(unsigned int x) {
    return __builtin_ctz(x);
}
long long ctz(long long x) {
    return __builtin_ctzll(x);
}
unsigned long long ctz(unsigned long long x) {
    return __builtin_ctzll(x);
}
int floor_log2(int x) {
    return 31 - clz(x);
}
unsigned floor_log2(unsigned x) {
    return 31 - clz(x);
}
long long floor_log2(long long x) {
    return 63 - clz(x);
}
unsigned long long floor_log2(unsigned long long x) {
    return 63 - clz(x);
}
template <typename T>
T mask_n(T x, T n) {
    T mask = ((T) 1 << n) - 1;
    return x & mask;
}
// ============
template <unsigned mod>
class NumberTheoreticTransform {
    static constexpr int calc_ex() {
        unsigned m = mod - 1;
        int ret = 0;
        while (!(m & 1)) {
            m >>= 1;
            ++ret;
        }
        return ret;
    }
    static constexpr int max_ex = calc_ex();
    std::array<ModInt<mod>, max_ex + 1> root;
    std::array<ModInt<mod>, max_ex + 1> inv_root;
    std::array<ModInt<mod>, max_ex + 2> inc;
    std::array<ModInt<mod>, max_ex + 2> inv_inc;
public:
    void dft(std::vector<ModInt<mod>> &a) const {
        int n = (int) a.size();
        int ex = ctz(n);
        for (int i = 0; i < ex; ++i) {
            int pr = 1 << (ex - 1 - i);
            int len = 1 << i;
            ModInt<mod> zeta(1);
            for (int j = 0; j < len; ++j) {
                int offset = j << (ex - i);
                for (int k = 0; k < pr; ++k) {
                    ModInt<mod> l = a[offset + k];
                    ModInt<mod> r = a[offset + k + pr] * zeta;
                    a[offset + k] = l + r;
                    a[offset + k + pr] = l - r;
                }
                zeta *= inc[ctz(~j)];
            }
        }
    }
    void idft(std::vector<ModInt<mod>> &a) const {
        int n = (int) a.size();
        int ex = ctz(n);
        for (int i = ex - 1; i >= 0; --i) {
            int pr = 1 << (ex - 1 - i);
            int len = 1 << i;
            ModInt<mod> zeta(1);
            for (int j = 0; j < len; ++j) {
                int offset = j << (ex - i);
                for (int k = 0; k < pr; ++k) {
                    ModInt<mod> l = a[offset + k];
                    ModInt<mod> r = a[offset + k + pr];
                    a[offset + k] = l + r;
                    a[offset + k + pr] = (l - r) * zeta;
                }
                zeta *= inv_inc[ctz(~j)];
            }
        }
        ModInt<mod> inv = ModInt<mod>::raw((unsigned) a.size()).inv();
        for (ModInt<mod> &ele : a) {
            ele *= inv;
        }
    }
    constexpr NumberTheoreticTransform() : root(), inv_root() {
        ModInt<mod> g = ModInt<mod>::raw(primitive_root<mod>()).pow((mod - 1) >> max_ex);
        root[max_ex] = g;
        inv_root[max_ex] = g.inv();
        for (int i = max_ex; i > 0; --i) {
            root[i - 1] = root[i] * root[i];
            inv_root[i - 1] = inv_root[i] * inv_root[i];
        }
        ModInt<mod> prod(1);
        for (int i = 2; i <= max_ex; ++i) {
            inc[i - 2] = root[i] * prod;
            prod *= inv_root[i];
        }
        prod = ModInt<mod>(1);
        for (int i = 2; i <= max_ex; ++i) {
            inv_inc[i - 2] = inv_root[i] * prod;
            prod *= root[i];
        }
    }
    std::vector<ModInt<mod>> multiply(
        std::vector<ModInt<mod>> a,
        std::vector<ModInt<mod>> b) const {
        if (a.empty() || b.empty())
            return std::vector<ModInt<mod>>();
        int siz = 1;
        int s = (int) (a.size() + b.size());
        while (siz < s) {
            siz <<= 1;
        }
        a.resize(siz, ModInt<mod>());
        b.resize(siz, ModInt<mod>());
        dft(a);
        dft(b);
        for (int i = 0; i < siz; ++i) {
            a[i] *= b[i];
        }
        idft(a);
        a.resize(s - 1);
        return a;
    }
};
template <unsigned mod>
class NTTMul {
    static constexpr NumberTheoreticTransform<mod> ntt = NumberTheoreticTransform<mod>();
public:
    static void dft(std::vector<ModInt<mod>> &a) {
        ntt.dft(a);
    }
    static void idft(std::vector<ModInt<mod>> &a) {
        ntt.idft(a);
    }
    static std::vector<ModInt<mod>> mul(
        std::vector<ModInt<mod>> lhs,
        std::vector<ModInt<mod>> rhs) {
        return ntt.multiply(std::move(lhs), std::move(rhs));
    }
};
// ============
using Mint = ModInt<mod998244353>;
constexpr NumberTheoreticTransform<mod998244353> NTT;
int main() {
    i32 h, w;
    cin >> h >> w;
    
    FactorialTable<Mint> table(h + w);
    
    const auto mk = [&](i32 n) -> Vec<Mint> {
        Vec<Mint> m(n + 1);
        REP(i, n + 1) {
            if (2 * i < n) {
                continue;
            }
            m[i] = table.choose(i, n - i);
        }
        REP(i, n + 1) {
            m[i] *= table.inv_fact(i);
        }
        return m;
    };
    Vec<Mint> a = mk(h);
    Vec<Mint> b = mk(w);
    Vec<Mint> c = NTT.multiply(a, b);
    Mint ans;
    REP(i, c.size()) {
        ans += c[i] * table.fact(i);
    }
    cout << ans << '\n';
}
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