結果

問題 No.1100 Boxes
ユーザー snrnsidysnrnsidy
提出日時 2021-05-30 04:13:19
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 147 ms / 2,000 ms
コード長 10,926 bytes
コンパイル時間 2,208 ms
コンパイル使用メモリ 204,836 KB
実行使用メモリ 81,664 KB
最終ジャッジ日時 2024-11-08 20:38:30
合計ジャッジ時間 8,863 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
このコードへのチャレンジ
（要ログイン）

テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 122 ms
81,408 KB
testcase_01 AC 121 ms
81,536 KB
testcase_02 AC 121 ms
81,536 KB
testcase_03 AC 122 ms
81,536 KB
testcase_04 AC 121 ms
81,664 KB
testcase_05 AC 121 ms
81,536 KB
testcase_06 AC 122 ms
81,536 KB
testcase_07 AC 121 ms
81,536 KB
testcase_08 AC 122 ms
81,536 KB
testcase_09 AC 121 ms
81,536 KB
testcase_10 AC 120 ms
81,664 KB
testcase_11 AC 121 ms
81,408 KB
testcase_12 AC 121 ms
81,536 KB
testcase_13 AC 121 ms
81,536 KB
testcase_14 AC 120 ms
81,664 KB
testcase_15 AC 122 ms
81,664 KB
testcase_16 AC 121 ms
81,408 KB
testcase_17 AC 120 ms
81,664 KB
testcase_18 AC 120 ms
81,536 KB
testcase_19 AC 122 ms
81,536 KB
testcase_20 AC 123 ms
81,536 KB
testcase_21 AC 129 ms
81,536 KB
testcase_22 AC 138 ms
81,536 KB
testcase_23 AC 129 ms
81,536 KB
testcase_24 AC 132 ms
81,664 KB
testcase_25 AC 135 ms
81,664 KB
testcase_26 AC 144 ms
81,408 KB
testcase_27 AC 139 ms
81,408 KB
testcase_28 AC 126 ms
81,664 KB
testcase_29 AC 142 ms
81,536 KB
testcase_30 AC 138 ms
81,536 KB
testcase_31 AC 129 ms
81,536 KB
testcase_32 AC 138 ms
81,536 KB
testcase_33 AC 147 ms
81,536 KB
testcase_34 AC 147 ms
81,536 KB
testcase_35 AC 121 ms
81,664 KB
testcase_36 AC 135 ms
81,536 KB
testcase_37 AC 121 ms
81,664 KB
testcase_38 AC 131 ms
81,536 KB
testcase_39 AC 145 ms
81,408 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h> 

using namespace std;

const long long int MOD = 998244353;
long long int f[5000001];
long long int invf[5000001];
namespace atcoder {

    namespace internal {

        // @param m `1 <= m`
        // @return x mod m
        constexpr long long safe_mod(long long x, long long m) {
            x %= m;
            if (x < 0) x += m;
            return x;
        }

        // Fast modular multiplication by barrett reduction
        // Reference: https://en.wikipedia.org/wiki/Barrett_reduction
        // NOTE: reconsider after Ice Lake
        struct barrett {
            unsigned int _m;
            unsigned long long im;

            // @param m `1 <= m < 2^31`
            explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

            // @return m
            unsigned int umod() const { return _m; }

            // @param a `0 <= a < m`
            // @param b `0 <= b < m`
            // @return `a * b % m`
            unsigned int mul(unsigned int a, unsigned int b) const {
                // [1] m = 1
                // a = b = im = 0, so okay

                // [2] m >= 2
                // im = ceil(2^64 / m)
                // -> im * m = 2^64 + r (0 <= r < m)
                // let z = a*b = c*m + d (0 <= c, d < m)
                // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
                // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
                // ((ab * im) >> 64) == c or c + 1
                unsigned long long z = a;
                z *= b;
#ifdef _MSC_VER
                unsigned long long x;
                _umul128(z, im, &x);
#else
                unsigned long long x =
                    (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
                unsigned int v = (unsigned int)(z - x * _m);
                if (_m <= v) v += _m;
                return v;
            }
        };

        // @param n `0 <= n`
        // @param m `1 <= m`
        // @return `(x ** n) % m`
        constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
            if (m == 1) return 0;
            unsigned int _m = (unsigned int)(m);
            unsigned long long r = 1;
            unsigned long long y = safe_mod(x, m);
            while (n) {
                if (n & 1) r = (r * y) % _m;
                y = (y * y) % _m;
                n >>= 1;
            }
            return r;
        }

        // Reference:
        // M. Forisek and J. Jancina,
        // Fast Primality Testing for Integers That Fit into a Machine Word
        // @param n `0 <= n`
        constexpr bool is_prime_constexpr(int n) {
            if (n <= 1) return false;
            if (n == 2 || n == 7 || n == 61) return true;
            if (n % 2 == 0) return false;
            long long d = n - 1;
            while (d % 2 == 0) d /= 2;
            constexpr long long bases[3] = { 2, 7, 61 };
            for (long long a : bases) {
                long long t = d;
                long long y = pow_mod_constexpr(a, t, n);
                while (t != n - 1 && y != 1 && y != n - 1) {
                    y = y * y % n;
                    t <<= 1;
                }
                if (y != n - 1 && t % 2 == 0) {
                    return false;
                }
            }
            return true;
        }
        template <int n> constexpr bool is_prime = is_prime_constexpr(n);

        // @param b `1 <= b`
        // @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
        constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
            a = safe_mod(a, b);
            if (a == 0) return { b, 0 };

            // Contracts:
            // [1] s - m0 * a = 0 (mod b)
            // [2] t - m1 * a = 0 (mod b)
            // [3] s * |m1| + t * |m0| <= b
            long long s = b, t = a;
            long long m0 = 0, m1 = 1;

            while (t) {
                long long u = s / t;
                s -= t * u;
                m0 -= m1 * u;  // |m1 * u| <= |m1| * s <= b

                // [3]:
                // (s - t * u) * |m1| + t * |m0 - m1 * u|
                // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
                // = s * |m1| + t * |m0| <= b

                auto tmp = s;
                s = t;
                t = tmp;
                tmp = m0;
                m0 = m1;
                m1 = tmp;
            }
            // by [3]: |m0| <= b/g
            // by g != b: |m0| < b/g
            if (m0 < 0) m0 += b / s;
            return { s, m0 };
        }

        // Compile time primitive root
        // @param m must be prime
        // @return primitive root (and minimum in now)
        constexpr int primitive_root_constexpr(int m) {
            if (m == 2) return 1;
            if (m == 167772161) return 3;
            if (m == 469762049) return 3;
            if (m == 754974721) return 11;
            if (m == 998244353) return 3;
            int divs[20] = {};
            divs[0] = 2;
            int cnt = 1;
            int x = (m - 1) / 2;
            while (x % 2 == 0) x /= 2;
            for (int i = 3; (long long)(i)*i <= x; i += 2) {
                if (x % i == 0) {
                    divs[cnt++] = i;
                    while (x % i == 0) {
                        x /= i;
                    }
                }
            }
            if (x > 1) {
                divs[cnt++] = x;
            }
            for (int g = 2;; g++) {
                bool ok = true;
                for (int i = 0; i < cnt; i++) {
                    if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                        ok = false;
                        break;
                    }
                }
                if (ok) return g;
            }
        }
        template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

        // @param n `n < 2^32`
        // @param m `1 <= m < 2^32`
        // @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
        unsigned long long floor_sum_unsigned(unsigned long long n,
            unsigned long long m,
            unsigned long long a,
            unsigned long long b) {
            unsigned long long ans = 0;
            while (true) {
                if (a >= m) {
                    ans += n * (n - 1) / 2 * (a / m);
                    a %= m;
                }
                if (b >= m) {
                    ans += n * (b / m);
                    b %= m;
                }

                unsigned long long y_max = a * n + b;
                if (y_max < m) break;
                // y_max < m * (n + 1)
                // floor(y_max / m) <= n
                n = (unsigned long long)(y_max / m);
                b = (unsigned long long)(y_max % m);
                std::swap(m, a);
            }
            return ans;
        }

    }  // namespace internal

}  // namespace atcoder


namespace atcoder {

    long long pow_mod(long long x, long long n, int m) {
        assert(0 <= n && 1 <= m);
        if (m == 1) return 0;
        internal::barrett bt((unsigned int)(m));
        unsigned int r = 1, y = (unsigned int)(internal::safe_mod(x, m));
        while (n) {
            if (n & 1) r = bt.mul(r, y);
            y = bt.mul(y, y);
            n >>= 1;
        }
        return r;
    }

    long long inv_mod(long long x, long long m) {
        assert(1 <= m);
        auto z = internal::inv_gcd(x, m);
        assert(z.first == 1);
        return z.second;
    }

    // (rem, mod)
    std::pair<long long, long long> crt(const std::vector<long long>& r,
        const std::vector<long long>& m) {
        assert(r.size() == m.size());
        int n = int(r.size());
        // Contracts: 0 <= r0 < m0
        long long r0 = 0, m0 = 1;
        for (int i = 0; i < n; i++) {
            assert(1 <= m[i]);
            long long r1 = internal::safe_mod(r[i], m[i]), m1 = m[i];
            if (m0 < m1) {
                std::swap(r0, r1);
                std::swap(m0, m1);
            }
            if (m0 % m1 == 0) {
                if (r0 % m1 != r1) return { 0, 0 };
                continue;
            }
            // assume: m0 > m1, lcm(m0, m1) >= 2 * max(m0, m1)

            // (r0, m0), (r1, m1) -> (r2, m2 = lcm(m0, m1));
            // r2 % m0 = r0
            // r2 % m1 = r1
            // -> (r0 + x*m0) % m1 = r1
            // -> x*u0*g = r1-r0 (mod u1*g) (u0*g = m0, u1*g = m1)
            // -> x = (r1 - r0) / g * inv(u0) (mod u1)

            // im = inv(u0) (mod u1) (0 <= im < u1)
            long long g, im;
            std::tie(g, im) = internal::inv_gcd(m0, m1);

            long long u1 = (m1 / g);
            // |r1 - r0| < (m0 + m1) <= lcm(m0, m1)
            if ((r1 - r0) % g) return { 0, 0 };

            // u1 * u1 <= m1 * m1 / g / g <= m0 * m1 / g = lcm(m0, m1)
            long long x = (r1 - r0) / g % u1 * im % u1;

            // |r0| + |m0 * x|
            // < m0 + m0 * (u1 - 1)
            // = m0 + m0 * m1 / g - m0
            // = lcm(m0, m1)
            r0 += x * m0;
            m0 *= u1;  // -> lcm(m0, m1)
            if (r0 < 0) r0 += m0;
        }
        return { r0, m0 };
    }

    long long floor_sum(long long n, long long m, long long a, long long b) {
        assert(0 <= n && n < (1LL << 32));
        assert(1 <= m && m < (1LL << 32));
        unsigned long long ans = 0;
        if (a < 0) {
            unsigned long long a2 = internal::safe_mod(a, m);
            ans -= 1ULL * n * (n - 1) / 2 * ((a2 - a) / m);
            a = a2;
        }
        if (b < 0) {
            unsigned long long b2 = internal::safe_mod(b, m);
            ans -= 1ULL * n * ((b2 - b) / m);
            b = b2;
        }
        return ans + internal::floor_sum_unsigned(n, m, a, b);
    }

}  // namespace atcoder

using namespace atcoder;

int main(void)
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    f[0] = 1;
    for (int i = 1; i <= 5000000; i++)
    {
        f[i] = ((f[i - 1] % MOD) * (i % MOD) % MOD);
        f[i] %= MOD;
    }
    invf[5000000] = inv_mod(f[5000000], MOD);
    for (int i = 5000000; i > 0; i--)
    {
        invf[i - 1] = ((invf[i] % MOD) * (i % MOD) % MOD);
        invf[i - 1] %= MOD;
    }

    long long int N, K;

    cin >> N >> K;

    long long int res = 0;

    for (int i = 1; i <= K; i++)
    {
        long long int val = pow_mod(MOD - 2, i - 1, MOD);
        long long int val2 = pow_mod(K - i, N, MOD);
        long long int num = f[K];
        num = ((num % MOD) * (invf[i] % MOD) % MOD);
        num %= MOD;
        num = ((num % MOD) * (invf[K-i] % MOD) % MOD);
        num %= MOD;
        num = ((num % MOD) * (val % MOD) % MOD);
        num %= MOD;
        num = ((num % MOD) * (val2 % MOD) % MOD);
        num %= MOD;
        res += num;
        res %= MOD;
    }

    cout << res << '\n';

    return 0;
}
0