結果

問題 No.995 タピオカオイシクナーレ
コンテスト
ユーザー oevl
提出日時 2020-04-19 15:53:08
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 52 ms / 2,000 ms
コード長 4,065 bytes
コンパイル時間 5,493 ms
コンパイル使用メモリ 203,384 KB
最終ジャッジ日時 2025-01-09 21:37:27
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 * 23
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;

template<int64_t MOD> class ModInt {
public:
    int64_t x;
    constexpr ModInt() : x(0) {}
    constexpr ModInt(int64_t v) : x((v % MOD + MOD) % MOD) {}
    constexpr ModInt operator - () const noexcept { return x ? MOD - x : 0;}
    constexpr ModInt operator + (const ModInt a) const noexcept { return ModInt(*this) += a;}
    constexpr ModInt operator - (const ModInt a) const noexcept { return ModInt(*this) -= a;}
    constexpr ModInt operator * (const ModInt a) const noexcept { return ModInt(*this) *= a;}
    constexpr ModInt operator / (const ModInt a) const noexcept { return ModInt(*this) /= a;}
    constexpr ModInt operator / (const int64_t a) const noexcept { return ModInt(*this) /= a;}
    constexpr ModInt operator += (const ModInt a) noexcept {
        x += a.x;
        if (x >= MOD) x -= MOD;
        return *this;
    }
    constexpr ModInt operator += (const int64_t a) noexcept {
        auto hs = ModInt<MOD>(a);
        (*this) += hs;
        return *this;
    }
    constexpr ModInt operator -= (const ModInt a) noexcept {
        if (x < a.x) x += MOD;
        x -= a.x;
        return *this;
    }
    constexpr ModInt operator -= (const int64_t a) noexcept {
        auto hs = ModInt<MOD>(a);
        (*this) -= hs;
        return *this;
    }
    constexpr ModInt operator *= (const ModInt a) noexcept {
        x = x * a.x % MOD;
        return *this;
    }
    constexpr ModInt operator *= (const int64_t a) noexcept {
        auto hs = ModInt<MOD>(a);
        (*this) *= hs;
        return *this;
    }
    constexpr ModInt &operator /= (ModInt a) noexcept {
        int64_t exp = MOD - 2;
        while (exp > 0) {
            if (exp & 1ul) *this *= a;
            a *= a;
            exp >>= 1ul;
        }
        return *this;
    }
    constexpr ModInt &operator /= (int64_t a) noexcept {
        auto hs = ModInt<MOD>(a);
        (*this) /= hs;
        return *this;
    }
    constexpr ModInt &operator ++ () noexcept {
        if (++x >= MOD) x -= MOD;
        return *this;
    }
    constexpr ModInt &operator -- () noexcept {
        if (x-- == 0) x += MOD;
        return *this;
    }
    constexpr bool operator < (const ModInt a) const noexcept { return x < a.x;}
    constexpr bool operator == (const ModInt a) const noexcept { return this->x == a.x;}
    constexpr bool operator != (const ModInt a) const noexcept { return !(*this == a);}
    friend istream &operator >> (istream &in, ModInt &m) {
        in >> m.x;
        if (m.x < 0) m.x += MOD;
        m.x %= MOD;
        return in;
    }
    friend ostream &operator << (ostream &out, const ModInt &p) { return out << p.x;}
    constexpr ModInt pow(int64_t p) const {
        ModInt ret(1);
        ModInt mul(x);
        while (p > 0) {
            if (p & 1ul) ret *= mul;
            mul *= mul;
            p >>= 1ul;
        }
        return ret;
    }
};

const int64_t MOD = 1000000007LL;
using mint = ModInt<MOD>;

using vec = vector<mint>;
using Matrix = vector<vec>;

Matrix Mul(Matrix A, Matrix B) {
    Matrix C(A.size(), vec(B[0].size()));
    for(int i = 0; i < A.size(); ++i) {
        for(int k = 0; k < B.size(); ++k) {
            for(int j = 0; j < B[0].size(); ++j) {
                C[i][j] += (A[i][k] * B[k][j]);
            }
        }
    }
    return C;
}

Matrix Pow(Matrix A, int64_t n) {
    int N = A.size();
    Matrix B(N, vec(N));
    for(int i = 0; i < N; ++i) B[i][i] = 1;
    while(n > 0) {
        if(n & 1) B = Mul(B, A);
        A = Mul(A, A);
        n >>= 1;
    }
    return B;
}

int main() {
    int N, M, p, q;
    int64_t K;
    cin >> N >> M >> K >> p >> q;
    vector<int> b(N);
    for(auto &e : b) cin >> e;
    Matrix A(2, vec(2));
    mint a = (mint)p / q;
    A[0][0] = (mint)-2 * a + 1; A[0][1] = a;
    A[1][0] = 0; A[1][1] = 1;
    A = Pow(A, K);
    mint ans = 0;
    mint P = A[0][0] + A[0][1];
    for(int i = 0; i < N; ++i) {
        if(i < M) ans += P * b[i];
        else ans += ((mint)1 - P) * b[i];
    }
    cout << ans << '\n';
    return 0;
}
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