結果

問題 No.2365 Present of good number
ユーザー erbowlerbowl
提出日時 2023-07-02 11:17:45
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 9 ms / 2,000 ms
コード長 7,104 bytes
コンパイル時間 3,190 ms
コンパイル使用メモリ 232,436 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-07-16 07:15:48
合計ジャッジ時間 4,134 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge4
このコードへのチャレンジ
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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 2 ms
5,248 KB
testcase_01 AC 2 ms
5,376 KB
testcase_02 AC 9 ms
5,376 KB
testcase_03 AC 9 ms
5,376 KB
testcase_04 AC 9 ms
5,376 KB
testcase_05 AC 9 ms
5,376 KB
testcase_06 AC 5 ms
5,376 KB
testcase_07 AC 7 ms
5,376 KB
testcase_08 AC 5 ms
5,376 KB
testcase_09 AC 4 ms
5,376 KB
testcase_10 AC 9 ms
5,376 KB
testcase_11 AC 2 ms
5,376 KB
testcase_12 AC 5 ms
5,376 KB
testcase_13 AC 8 ms
5,376 KB
testcase_14 AC 7 ms
5,376 KB
testcase_15 AC 4 ms
5,376 KB
testcase_16 AC 2 ms
5,376 KB
testcase_17 AC 2 ms
5,376 KB
testcase_18 AC 2 ms
5,376 KB
testcase_19 AC 2 ms
5,376 KB
testcase_20 AC 2 ms
5,376 KB
testcase_21 AC 2 ms
5,376 KB
testcase_22 AC 3 ms
5,376 KB
testcase_23 AC 7 ms
5,376 KB
testcase_24 AC 2 ms
5,376 KB
testcase_25 AC 4 ms
5,376 KB
testcase_26 AC 7 ms
5,376 KB
testcase_27 AC 5 ms
5,376 KB
testcase_28 AC 3 ms
5,376 KB
testcase_29 AC 8 ms
5,376 KB
testcase_30 AC 4 ms
5,376 KB
testcase_31 AC 2 ms
5,376 KB
testcase_32 AC 2 ms
5,376 KB
testcase_33 AC 1 ms
5,376 KB
testcase_34 AC 2 ms
5,376 KB
testcase_35 AC 2 ms
5,376 KB
testcase_36 AC 8 ms
5,376 KB
testcase_37 AC 9 ms
5,376 KB
testcase_38 AC 6 ms
5,376 KB
testcase_39 AC 6 ms
5,376 KB
testcase_40 AC 9 ms
5,376 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 # 

typedef long long ll;
typedef long double ld;
#include <bits/stdc++.h>
using namespace std;
#define int long long


struct Eratos {
    vector<int> primes;
    vector<bool> isprime;
    vector<int> mebius;
    vector<int> min_factor;

    Eratos(int MAX) : primes(),
                      isprime(MAX+1, true),
                      mebius(MAX+1, 1),
                      min_factor(MAX+1, -1) {
        isprime[0] = isprime[1] = false;
        min_factor[0] = 0, min_factor[1] = 1;
        for (int i = 2; i <= MAX; ++i) {
            if (!isprime[i]) continue;
            primes.push_back(i);
            mebius[i] = -1;
            min_factor[i] = i;
            for (int j = i*2; j <= MAX; j += i) {
                isprime[j] = false;
                if ((j / i) % i == 0) mebius[j] = 0;
                else mebius[j] = -mebius[j];
                if (min_factor[j] == -1) min_factor[j] = i;
            }
        }
    }

    // prime factorization
    vector<pair<int,int>> prime_factors(int n) {
        vector<pair<int,int> > res;
        while (n != 1) {
            int prime = min_factor[n];
            int exp = 0;
            while (min_factor[n] == prime) {
                ++exp;
                n /= prime;
            }
            res.push_back(make_pair(prime, exp));
        }
        return res;
    }

    // enumerate divisors
    vector<int> divisors(int n) {
        vector<int> res({1});
        auto pf = prime_factors(n);
        for (auto p : pf) {
            int n = (int)res.size();
            for (int i = 0; i < n; ++i) {
                int v = 1;
                for (int j = 0; j < p.second; ++j) {
                    v *= p.first;
                    res.push_back(res[i] * v);
                }
            }
        }
        return res;
    }
};





const long long MOD = 1e9+7;
long long modinv(long long a, long long mod) {
    long long b = mod, u = 1, v = 0;
    while (b) {
        long long t = a/b;
        a -= t*b; swap(a, b);
        u -= t*v; swap(u, v);
    }
    u %= mod;
    if (u < 0) u += mod;
    return u;
}

// matrix
template<int MOD> struct Matrix {
    vector<vector<long long> > val;
    Matrix(int n, int m, long long x = 0) : val(n, vector<long long>(m, x)) {}
    void init(int n, int m, long long x = 0) {val.assign(n, vector<long long>(m, x));}
    size_t size() const {return val.size();}
    inline vector<long long>& operator [] (int i) {return val[i];}
};

template<int MOD> ostream& operator << (ostream& s, Matrix<MOD> A) {
    s << endl; 
    for (int i = 0; i < A.size(); ++i) {
        for (int j = 0; j < A[i].size(); ++j) {
            s << A[i][j] << ", ";
        }
        s << endl;
    }
    return s;
}

template<int MOD> Matrix<MOD> operator * (Matrix<MOD> A, Matrix<MOD> B) {
    Matrix<MOD> R(A.size(), B[0].size());
    for (int i = 0; i < A.size(); ++i) 
        for (int j = 0; j < B[0].size(); ++j)
            for (int k = 0; k < B.size(); ++k) 
                R[i][j] = (R[i][j] + A[i][k] * B[k][j] % MOD) % MOD; 
    return R;
}

template<int MOD> Matrix<MOD> pow(Matrix<MOD> A, long long n) {
    Matrix<MOD> R(A.size(), A.size());
    for (int i = 0; i < A.size(); ++i) R[i][i] = 1;
    while (n > 0) {
        if (n & 1) R = R * A;
        A = A * A;
        n >>= 1;
    }
    return R;
}



// modint
template<int MOD> struct Fp {
    // inner value
    long long val;
    
    // constructor
    constexpr Fp() noexcept : val(0) { }
    constexpr Fp(long long v) noexcept : val(v % MOD) {
        if (val < 0) val += MOD;
    }
    constexpr long long get() const noexcept { return val; }
    constexpr int get_mod() const noexcept { return MOD; }
    
    // arithmetic operators
    constexpr Fp operator - () const noexcept {
        return val ? MOD - val : 0;
    }
    constexpr Fp operator + (const Fp &r) const noexcept { return Fp(*this) += r; }
    constexpr Fp operator - (const Fp &r) const noexcept { return Fp(*this) -= r; }
    constexpr Fp operator * (const Fp &r) const noexcept { return Fp(*this) *= r; }
    constexpr Fp operator / (const Fp &r) const noexcept { return Fp(*this) /= r; }
    constexpr Fp& operator += (const Fp &r) noexcept {
        val += r.val;
        if (val >= MOD) val -= MOD;
        return *this;
    }
    constexpr Fp& operator -= (const Fp &r) noexcept {
        val -= r.val;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr Fp& operator *= (const Fp &r) noexcept {
        val = val * r.val % MOD;
        return *this;
    }
    constexpr Fp& operator /= (const Fp &r) noexcept {
        long long a = r.val, b = MOD, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b, swap(a, b);
            u -= t * v, swap(u, v);
        }
        val = val * u % MOD;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr Fp pow(long long n) const noexcept {
        Fp res(1), mul(*this);
        while (n > 0) {
            if (n & 1) res *= mul;
            mul *= mul;
            n >>= 1;
        }
        return res;
    }
    constexpr Fp inv() const noexcept {
        Fp res(1), div(*this);
        return res / div;
    }

    // other operators
    constexpr bool operator == (const Fp &r) const noexcept {
        return this->val == r.val;
    }
    constexpr bool operator != (const Fp &r) const noexcept {
        return this->val != r.val;
    }
    friend constexpr istream& operator >> (istream &is, Fp<MOD> &x) noexcept {
        is >> x.val;
        x.val %= MOD;
        if (x.val < 0) x.val += MOD;
        return is;
    }
    friend constexpr ostream& operator << (ostream &os, const Fp<MOD> &x) noexcept {
        return os << x.val;
    }
    friend constexpr Fp<MOD> modpow(const Fp<MOD> &r, long long n) noexcept {
        return r.pow(n);
    }
    friend constexpr Fp<MOD> modinv(const Fp<MOD> &r) noexcept {
        return r.inv();
    }
};


signed main(){
    using mint = Fp<MOD>;
    ll n,k;
    std::cin >> n>>k;
    Eratos era(n+10);
    
    set<ll> p;
    queue<ll> q;
    for (auto e : era.prime_factors(n)) {
        q.push(e.first);
        p.insert(e.first);
    }
    while(q.size()){
        auto now = q.front();q.pop();
        auto es = era.prime_factors(now);
        for (auto e : es) {
            for (auto ee : era.prime_factors(e.first+1)) {
                if(p.find(ee.first)==p.end()){
                    p.insert(ee.first);
                    q.push(ee.first);
                }
            }
        }
    }
    Matrix<MOD-1> m(p.size(), p.size(), 0);
    unordered_map<ll,ll> pind;
    ll ind = 0;
    for (auto e : p) {
        pind[e] = ind;
        ind++;
    }
    for (auto e : p) {
        for (auto ee : era.prime_factors(e+1)) {
            m[pind[e]][pind[ee.first]] += ee.second;
        }
    }
    Matrix<MOD-1> c(1, p.size(), 0);

    for (auto e : era.prime_factors(n)) {
        c[0][pind[e.first]] += e.second;
    }
    
    auto res = c*pow(m,k);
    mint ans = 1;
    
    for (auto e : p) {
        ans *= mint(e).pow(res[0][pind[e]]);
    }
    std::cout << ans << std::endl;
    
}
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