結果

問題 No.213 素数サイコロと合成数サイコロ (3-Easy)
コンテスト
ユーザー maine_honzuki
提出日時 2020-12-23 00:00:56
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 26 ms / 3,000 ms
コード長 8,025 bytes
コンパイル時間 3,423 ms
コンパイル使用メモリ 223,564 KB
最終ジャッジ日時 2025-01-17 06:15:52
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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ファイルパターン 結果
other AC * 2
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ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
using ll = long long;

template <int mod>
struct NumberTheoreticTransform {
private:
    vector<int> rev, rts;
    int base, max_base, root;
    inline int mod_add(int a, int b) {
        a += b;
        if (a >= mod)
            a -= mod;
        return a;
    }
    inline int mod_mul(int a, int b) {
        return (int)((1ull * a * b) % (signed long long)mod);
    }
    inline int mod_pow(int a, int n) {
        int ret = 1;
        while (n) {
            if (n & 1)
                ret = mod_mul(ret, a);
            a = mod_mul(a, a);
            n >>= 1;
        }
        return ret;
    }
    inline int mod_inv(int a) {
        return mod_pow(a, mod - 2);
    }

public:
    NumberTheoreticTransform() : rev{0, 1}, rts{0, 1}, base(1) {
        assert(mod >= 3 && (mod & 1) == 1);
        int tmp = mod - 1;
        max_base = 0;
        while (tmp % 2 == 0) {
            tmp >>= 1;
            max_base++;
        }
        root = 2;
        while (mod_pow(root, (mod - 1) >> 1) == 1)
            root++;
        assert(mod_pow(root, mod - 1) == 1);
        root = mod_pow(root, (mod - 1) >> max_base);
    }

private:
    void ensure_base(int nbase) {
        if (nbase <= base)
            return;
        assert(nbase <= max_base);
        rev.resize(1 << nbase);
        rts.resize(1 << nbase);
        for (int i = 0; i < (1 << nbase); i++) {
            rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
        }
        while (base < nbase) {
            int z = mod_pow(root, 1 << (max_base - 1 - base));
            for (int i = 1 << (base - 1); i < (1 << base); i++) {
                rts[i << 1] = rts[i];
                rts[(i << 1) + 1] = mod_mul(rts[i], z);
            }
            base++;
        }
    }
    void ntt(vector<int>& a) {
        const int n = (int)a.size();
        assert((n & (n - 1)) == 0);
        int zeros = __builtin_ctz(n);
        ensure_base(zeros);
        int shift = base - zeros;
        for (int i = 0; i < n; i++) {
            if (i < (rev[i] >> shift))
                swap(a[i], a[rev[i] >> shift]);
        }
        for (int k = 1; k < n; k <<= 1) {
            for (int i = 0; i < n; i += 2 * k) {
                for (int j = 0; j < k; j++) {
                    int z = mod_mul(a[i + j + k], rts[j + k]);
                    a[i + j + k] = mod_add(a[i + j], mod - z);
                    a[i + j] = mod_add(a[i + j], z);
                }
            }
        }
    }

public:
    vector<int> multiply(vector<int> a, vector<int> b) {
        if (a.empty() || b.empty())
            return {};
        bool eq = (a == b);
        int need = (int)(a.size() + b.size() - 1);
        int nbase = 1;
        while ((1 << nbase) < need)
            nbase++;
        ensure_base(nbase);
        int sz = 1 << nbase;
        a.resize(sz, 0);
        b.resize(sz, 0);
        ntt(a);
        if (eq)
            b = a;
        else
            ntt(b);
        int inv_sz = mod_inv(sz);
        for (int i = 0; i < sz; i++) {
            a[i] = mod_mul(a[i], mod_mul(b[i], inv_sz));
        }
        reverse(a.begin() + 1, a.end());
        ntt(a);
        a.resize(need);
        return a;
    }
    vector<long long> multiply(vector<long long> a, vector<long long> b) {
        vector<int> A(a.size()), B(b.size());
        for (int i = 0; i < (int)a.size(); i++) {
            A[i] = (int)(a[i] % mod);
        }
        for (int i = 0; i < (int)b.size(); i++) {
            B[i] = (int)(b[i] % mod);
        }
        A = multiply(A, B);
        a.resize(A.size());
        for (int i = 0; i < (int)A.size(); i++)
            a[i] = A[i];
        return a;
    }
};

template <typename T>
T extgcd(T a, T b, T& x, T& y) {
    if (b) {
        T d = extgcd(b, a % b, y, x);
        y -= a / b * x;
        return d;
    } else {
        x = 1;
        y = 0;
        return a;
    }
}
template <typename T>
T modinv(T a, T m) {
    T x, y;
    T d = extgcd(a, m, x, y);
    if (d != 1)
        return -1;
    x %= m;
    if (x < 0)
        x += m;
    return x;
}
template <typename T>
T garner_mod(vector<T> r, vector<T> m, ll MOD) {
    assert(r.size() == m.size());
    int N = (int)r.size();
    vector<T> v(N);
    v[0] = r[0] % m[0];
    for (int i = 1; i < N; i++) {
        T prod = 1;
        for (int j = 0; j < i; j++) {
            (prod *= m[j]) %= m[i];
        }
        T tmp = v[i - 1];
        for (int j = i - 2; j >= 0; j--) {
            tmp = (tmp * m[j] % m[i] + v[j]) % m[i];
        }
        v[i] = (r[i] - tmp) * modinv(prod, m[i]) % m[i];
        if (v[i] < 0)
            v[i] += m[i];
    }
    T ret = 0;
    for (int i = N - 1; i >= 0; i--) {
        ret = (ret * m[i] % MOD + v[i]) % MOD;
    }
    return ret;
}

template <int mod>
struct ArbitraryModConvolution {
private:
    const int MOD0 = 167772161, MOD1 = 469762049, MOD2 = 754974721;
    NumberTheoreticTransform<167772161> NTT0;
    NumberTheoreticTransform<469762049> NTT1;
    NumberTheoreticTransform<754974721> NTT2;

public:
    ArbitraryModConvolution() {}
    vector<ll> multiply(vector<ll> a, vector<ll> b) {
        if (a.empty() || b.empty())
            return {};
        auto V0 = NTT0.multiply(a, b), V1 = NTT1.multiply(a, b), V2 = NTT2.multiply(a, b);
        int N = (int)V0.size();
        vector<ll> res(N);
        //vector<ll> v(3);
        //ll prod, tmp;
        for (int i = 0; i < N; i++) {
            vector<ll> r{V0[i], V1[i], V2[i]}, m{MOD0, MOD1, MOD2};
            res[i] = garner_mod<ll>(r, m, mod);
            /*
            v[0] = V0[i] % MOD0;
            prod = MOD0 % MOD1;
            tmp = v[0];
            v[1] = (V1[i] - tmp) * modinv<ll>(prod, MOD1) % MOD1;
            if (v[1] < 0)
                v[1] += MOD1;
            prod = ((MOD0 % MOD1) * MOD1) % MOD2;
            tmp = v[1];
            tmp = (v[1] * MOD0 % MOD2 + v[0]) % MOD0;
            v[2] = (V2[i] - tmp) * modinv<ll>(prod, MOD2) % MOD2;
            if (v[2] < 0)
                v[2] += MOD2;
            res[i] = (res[i] * MOD2 % mod + v[2]) % mod;
            res[i] = (res[i] * MOD1 % mod + v[1]) % mod;
            res[i] = (res[i] * MOD0 % mod + v[0]) % mod;
            */
        }
        return res;
    }
};

template <class NTT>
ll coef(vector<ll> P, vector<ll> Q, ll N, ll MOD) {
    //[x^N]P(x)/Q(x)
    //Q(0) = 1
    NTT ntt;
    vector<ll> Qmin, V, U;
    while (N) {
        Qmin = Q;
        for (int i = 1; i < (int)Qmin.size(); i += 2)
            Qmin[i] = (MOD - Qmin[i]) % MOD;
        V = ntt.multiply(Q, Qmin);
        U = ntt.multiply(P, Qmin);
        P.clear();
        Q.clear();
        for (int i = 0; i < (int)V.size(); i += 2) {
            Q.emplace_back(V[i]);
        }
        if (N % 2 == 0) {
            for (int i = 0; i < (int)U.size(); i += 2)
                P.emplace_back(U[i]);
        } else {
            for (int i = 1; i < (int)U.size(); i += 2)
                P.emplace_back(U[i]);
        }
        N /= 2;
    }
    return P[0];
}

int main() {
    ll N;
    int P, C;
    cin >> N >> P >> C;
    const int MOD = 1e9 + 7;
    vector<int> dice1{2, 3, 5, 7, 11, 13}, dice2{4, 6, 8, 9, 10, 12};

    auto calc = [&MOD](vector<int> dice, int P) {
        int N = P * dice.back() + 1;
        vector<vector<ll>> dp(P + 1, vector<ll>(N));
        dp[0][0] = 1;
        for (auto& x : dice) {
            for (int i = 0; i < P; i++) {
                for (int j = 0; j < N - x; j++) {
                    (dp[i + 1][j + x] += dp[i][j]) %= MOD;
                }
            }
        }
        return dp[P];
    };

    using NTT = ArbitraryModConvolution<MOD>;
    NTT ntt;
    auto X = calc(dice1, P), Y = calc(dice2, C);
    auto Z = ntt.multiply(X, Y);

    vector<ll> T = Z;
    (T[0] += MOD - 1) %= MOD;
    for (auto& x : T)
        ((x *= -1) += MOD) %= MOD;

    vector<ll> S = Z;
    S[0] += 1;
    for (int i = (int)S.size() - 2; i >= 0; i--)
        (S[i] += S[i + 1]) %= MOD;
    S[0] = 0;

    cout << coef<NTT>(S, T, N, MOD) << endl;
}
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