結果

問題 No.1112 冥界の音楽
ユーザー kimiyukikimiyuki
提出日時 2020-07-10 22:03:15
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 13 ms / 2,000 ms
コード長 6,535 bytes
コンパイル時間 2,031 ms
コンパイル使用メモリ 196,560 KB
最終ジャッジ日時 2025-01-11 18:31:45
ジャッジサーバーID
（参考情報） 		judge3 / judge3
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ファイルパターン 結果
sample AC * 3
other AC * 34
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 # 

#line 1 "main.cpp"
#include <bits/stdc++.h>
#line 2 "/home/user/Library/utils/macros.hpp"
#define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i))
#define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i))
#define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i))
#define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i))
#define ALL(x) std::begin(x), std::end(x)
#line 4 "/home/user/Library/modulus/modpow.hpp"

inline int32_t modpow(uint_fast64_t x, uint64_t k, int32_t MOD) {
    assert (/* 0 <= x and */ x < (uint_fast64_t)MOD);
    uint_fast64_t y = 1;
    for (; k; k >>= 1) {
        if (k & 1) (y *= x) %= MOD;
        (x *= x) %= MOD;
    }
    assert (/* 0 <= y and */ y < (uint_fast64_t)MOD);
    return y;
}
#line 5 "/home/user/Library/modulus/modinv.hpp"

inline int32_t modinv_nocheck(int32_t value, int32_t MOD) {
    assert (0 <= value and value < MOD);
    if (value == 0) return -1;
    int64_t a = value, b = MOD;
    int64_t x = 0, y = 1;
    for (int64_t u = 1, v = 0; a; ) {
        int64_t q = b / a;
        x -= q * u; std::swap(x, u);
        y -= q * v; std::swap(y, v);
        b -= q * a; std::swap(b, a);
    }
    if (not (value * x + MOD * y == b and b == 1)) return -1;
    if (x < 0) x += MOD;
    assert (0 <= x and x < MOD);
    return x;
}

inline int32_t modinv(int32_t x, int32_t MOD) {
    int32_t y = modinv_nocheck(x, MOD);
    assert (y != -1);
    return y;
}
#line 4 "/home/user/Library/modulus/mint_core.hpp"

/**
 * @brief quotient ring / 剰余環 $\mathbb{Z}/n\mathbb{Z}$
 */
template <int32_t MOD>
struct mint {
    int32_t value;
    mint() : value() {}
    mint(int64_t value_) : value(value_ < 0 ? value_ % MOD + MOD : value_ >= MOD ? value_ % MOD : value_) {}
    mint(int32_t value_, std::nullptr_t) : value(value_) {}
    explicit operator bool() const { return value; }
    inline mint<MOD> operator + (mint<MOD> other) const { return mint<MOD>(*this) += other; }
    inline mint<MOD> operator - (mint<MOD> other) const { return mint<MOD>(*this) -= other; }
    inline mint<MOD> operator * (mint<MOD> other) const { return mint<MOD>(*this) *= other; }
    inline mint<MOD> & operator += (mint<MOD> other) { this->value += other.value; if (this->value >= MOD) this->value -= MOD; return *this; }
    inline mint<MOD> & operator -= (mint<MOD> other) { this->value -= other.value; if (this->value <    0) this->value += MOD; return *this; }
    inline mint<MOD> & operator *= (mint<MOD> other) { this->value = (uint_fast64_t)this->value * other.value % MOD; return *this; }
    inline mint<MOD> operator - () const { return mint<MOD>(this->value ? MOD - this->value : 0, nullptr); }
    inline bool operator == (mint<MOD> other) const { return value == other.value; }
    inline bool operator != (mint<MOD> other) const { return value != other.value; }
    inline mint<MOD> pow(uint64_t k) const { return mint<MOD>(modpow(value, k, MOD), nullptr); }
    inline mint<MOD> inv() const { return mint<MOD>(modinv(value, MOD), nullptr); }
    inline mint<MOD> operator / (mint<MOD> other) const { return *this * other.inv(); }
    inline mint<MOD> & operator /= (mint<MOD> other) { return *this *= other.inv(); }
};
template <int32_t MOD> mint<MOD> operator + (int64_t value, mint<MOD> n) { return mint<MOD>(value) + n; }
template <int32_t MOD> mint<MOD> operator - (int64_t value, mint<MOD> n) { return mint<MOD>(value) - n; }
template <int32_t MOD> mint<MOD> operator * (int64_t value, mint<MOD> n) { return mint<MOD>(value) * n; }
template <int32_t MOD> mint<MOD> operator / (int64_t value, mint<MOD> n) { return mint<MOD>(value) / n; }
template <int32_t MOD> std::istream & operator >> (std::istream & in, mint<MOD> & n) { int64_t value; in >> value; n = value; return in; }
template <int32_t MOD> std::ostream & operator << (std::ostream & out, mint<MOD> n) { return out << n.value; }
#line 5 "/home/user/Library/number/matrix_template.hpp"

template <typename T, size_t H, size_t W>
using matrix = std::array<std::array<T, W>, H>;

template <typename T, size_t A, size_t B, size_t C>
matrix<T, A, C> operator * (matrix<T, A, B> const & a, matrix<T, B, C> const & b) {
    matrix<T, A, C> c = {};
    REP (y, A) REP (z, B) REP (x, C) c[y][x] += a[y][z] * b[z][x];
    return c;
}
template <typename T, size_t H, size_t W>
std::array<T, H> operator * (matrix<T, H, W> const & a, std::array<T, W> const & b) {
    std::array<T, H> c = {};
    REP (y, H) REP (z, W) c[y] += a[y][z] * b[z];
    return c;
}

template <typename T, size_t H, size_t W>
matrix<T, H, W> operator + (matrix<T, H, W> const & a, matrix<T, H, W> const & b) {
    matrix<T, H, W> c;
    REP (y, H) REP (x, W) c[y][x] = a[y][x] + b[y][x];
    return c;
}

template <typename T, size_t N>
std::array<T, N> operator + (std::array<T, N> const & a, std::array<T, N> const & b) {
    std::array<T, N> c;
    REP (i, N) c[i] = a[i] + b[i];
    return c;
}

template <typename T, size_t H, size_t W>
matrix<T, H, W> zero_matrix() {
    return {};
}

template <typename T, size_t N>
matrix<T, N, N> unit_matrix() {
    matrix<T, N, N> a = {};
    REP (i, N) a[i][i] = 1;
    return a;
}

template <typename T, size_t N>
matrix<T, N, N> powmat(matrix<T, N, N> x, int64_t k) {
    matrix<T, N, N> y = unit_matrix<T, N>();
    for (; k; k >>= 1) {
        if (k & 1) y = y * x;
        x = x * x;
    }
    return y;
}
#line 5 "main.cpp"
using namespace std;

constexpr int MOD = 1000000007;
mint<MOD> solve(int k, int m, int64_t n, const vector<int> & p, const vector<int> & q, const vector<int> & r) {
    constexpr int K = 6;
    assert (k <= K);
    auto pack = [&](int a, int b) {
        return a * K + b;
    };
    matrix<mint<MOD>, K * K, K * K> f = {};
    REP (i, m) {
        f[pack(q[i], r[i])][pack(p[i], q[i])] += 1;
    }
    array<mint<MOD>, K * K> x = {};
    REP (b, K) {
        x[pack(0, b)] += 1;
    }
    array<mint<MOD>, K * K> y = powmat(f, n - 2) * x;
    mint<MOD> ans = 0;
    REP (a, K) {
        ans += y[pack(a, 0)];
    }
    return ans;
}

// generated by online-judge-template-generator v4.4.0 (https://github.com/kmyk/online-judge-template-generator)
int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    constexpr char endl = '\n';
    int K;
    int M;
    int64_t N;
    cin >> K >> M;
    vector<int> P(M), Q(M), R(M);
    cin >> N;
    REP (i, M) {
        cin >> P[i] >> Q[i] >> R[i];
        -- P[i];
        -- Q[i];
        -- R[i];
    }
    auto ans = solve(K, M, N, P, Q, R);
    cout << ans << endl;
    return 0;
}
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