#478479 (C++14) No.1050 Zero (Maximum)

• 問題: No.1050 Zero (Maximum)
• ユーザー: ミドリムシ
• 提出日時: 2020-05-08 21:50:50
• 言語: C++14 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 21 ms / 2,000 ms
• コード長: 9,134 bytes
• コンパイル時間: 1,827 ms
• コンパイル使用メモリ: 178,044 KB
• 実行使用メモリ: 6,944 KB
• 最終ジャッジ日時: 2024-07-04 00:30:12
• 合計ジャッジ時間: 2,325 ms
• ジャッジサーバーID （参考情報）: judge4 / judge3

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 6,816 KB
testcase_01	AC	2 ms; 6,940 KB
testcase_02	AC	7 ms; 6,940 KB
testcase_03	AC	5 ms; 6,940 KB
testcase_04	AC	13 ms; 6,944 KB
testcase_05	AC	15 ms; 6,940 KB
testcase_06	AC	7 ms; 6,944 KB
testcase_07	AC	9 ms; 6,940 KB
testcase_08	AC	2 ms; 6,940 KB
testcase_09	AC	5 ms; 6,940 KB
testcase_10	AC	18 ms; 6,944 KB
testcase_11	AC	13 ms; 6,940 KB
testcase_12	AC	2 ms; 6,944 KB
testcase_13	AC	2 ms; 6,940 KB
testcase_14	AC	2 ms; 6,940 KB
testcase_15	AC	2 ms; 6,944 KB
testcase_16	AC	18 ms; 6,940 KB
testcase_17	AC	21 ms; 6,940 KB

ソースコード

#include <bits/stdc++.h>
using namespace std;
using lint = long long;
constexpr lint mod = 1e9 + 7;
#define all(x) (x).begin(), (x).end()
#define bitcount(n) __builtin_popcountl((lint)(n))
#define fcout cout << fixed << setprecision(15)
#define highest(x) (63 - __builtin_clzl(x))
#define rep(i, n) for(int i = 0; i < int(n); i++)
#define rep2(i, l, r) for(int i = int(l); i < int(r); i++)
#define repr(i, n) for(int i = int(n) - 1; i >= 0; i--)
#define repr2(i, l, r) for(int i = int(r) - 1; i >= int(l); i--)
constexpr int inf9 = 1e9; constexpr lint inf18 = 1e18;
inline void YES(bool condition){ if(condition) cout << "YES" << endl; else cout << "NO" << endl; }
inline void Yes(bool condition){ if(condition) cout << "Yes" << endl; else cout << "No" << endl; }
inline void assert_NO(bool condition){ if(!condition){ cout << "NO" << endl; exit(0); } }
inline void assert_No(bool condition){ if(!condition){ cout << "No" << endl; exit(0); } }
inline void assert_minus_1(bool condition){ if(!condition){ cout << -1 << endl; exit(0); } }
lint power(lint base, lint exponent, lint module){ if(exponent % 2){ return power(base, exponent - 1, module) * base % module; }else if(exponent){ lint root_ans = power(base, exponent / 2, module); return root_ans * root_ans % module; }else{ return 1; }}
struct position{ int y, x; }; position mv[4] = {{0, -1}, {1, 0}, {0, 1}, {-1, 0}}; // double euclidean(position first, position second){ return sqrt((second.x - first.x) * (second.x - first.x) + (second.y - first.y) * (second.y - first.y)); }
template<class T, class U> string to_string(pair<T, U> x){ return to_string(x.first) + "," + to_string(x.second); } string to_string(string x){ return x; }
template<class itr> void array_output(itr start, itr goal){ string ans; for(auto i = start; i != goal; i++) ans += to_string(*i) + " "; if(!ans.empty()) ans.pop_back(); cout << ans << endl; }
template<class itr> void cins(itr first, itr last){ for(auto i = first; i != last; i++){ cin >> (*i); } }
template<class T> T gcd(T a, T b){ if(b) return gcd(b, a % b); else return a; }
template<class T> T lcm(T a, T b){ return a / gcd(a, b) * b; }
struct combination{ vector<lint> fact, inv; combination(int sz) : fact(sz + 1), inv(sz + 1){ fact[0] = 1; for(int i = 1; i <= sz; i++){ fact[i] = fact[i - 1] * i % mod; } inv[sz] = power(fact[sz], mod - 2, mod); for(int i = sz - 1; i >= 0; i--){ inv[i] = inv[i + 1] * (i + 1) % mod; } } lint P(int n, int r){ if(r < 0 || n < r) return 0; return (fact[n] * inv[n - r] % mod); } lint C(int p, int q){ if(q < 0 || p < q) return 0; return (fact[p] * inv[q] % mod * inv[p - q] % mod); } };
template<class itr> bool next_sequence(itr first, itr last, int max_bound){ itr now = last; while(now != first){ now--; (*now)++; if((*now) == max_bound){ (*now) = 0; }else{ return true; } } return false; }
template<class itr, class itr2> bool next_sequence2(itr first, itr last, itr2 first2, itr2 last2){ itr now = last; itr2 now2 = last2; while(now != first){ now--, now2--; (*now)++; if((*now) == (*now2)){ (*now) = 0; }else{ return true; } } return false; }
template<class T> bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b){ if(b < a){ a = b; return 1; } return 0; }
inline int at(lint i, int j){ return (i >> j) & 1; }
random_device rnd;
bool is_in_board(lint y, lint x, lint H, lint W){ return (0 <= y && y < H && 0 <= x && x < W); }

template< int mod >
struct ModInt {
    int x;
    
    ModInt() : x(0) {}
    
    ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
    
    ModInt &operator+=(const ModInt &p) {
        if((x += p.x) >= mod) x -= mod;
        return *this;
    }
    
    ModInt &operator-=(const ModInt &p) {
        if((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }
    
    ModInt &operator*=(const ModInt &p) {
        x = (int) (1LL * x * p.x % mod);
        return *this;
    }
    
    ModInt &operator/=(const ModInt &p) {
        *this *= p.inverse();
        return *this;
    }
    
    ModInt operator-() const { return ModInt(-x); }
    
    ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
    
    ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
    
    ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
    
    ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
    
    bool operator==(const ModInt &p) const { return x == p.x; }
    
    bool operator!=(const ModInt &p) const { return x != p.x; }
    
    ModInt inverse() const {
        int a = x, b = mod, u = 1, v = 0, t;
        while(b > 0) {
            t = a / b;
            swap(a -= t * b, b);
            swap(u -= t * v, v);
        }
        return ModInt(u);
    }
    
    ModInt pow(int64_t n) const {
        ModInt ret(1), mul(x);
        while(n > 0) {
            if(n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }
    
    friend ostream &operator<<(ostream &os, const ModInt &p) {
        return os << p.x;
    }
    
    friend istream &operator>>(istream &is, ModInt &a) {
        int64_t t;
        is >> t;
        a = ModInt< mod >(t);
        return (is);
    }
    
    static int get_mod() { return mod; }
};

using modint = ModInt< mod >;

template< class T >
struct Matrix {
    vector< vector< T > > A;
    
    Matrix() {}
    
    Matrix(size_t n, size_t m) : A(n, vector< T >(m, 0)) {}
    
    Matrix(size_t n) : A(n, vector< T >(n, 0)) {};
    
    size_t height() const {
        return (A.size());
    }
    
    size_t width() const {
        return (A[0].size());
    }
    
    inline const vector< T > &operator[](int k) const {
        return (A.at(k));
    }
    
    inline vector< T > &operator[](int k) {
        return (A.at(k));
    }
    
    static Matrix I(size_t n) {
        Matrix mat(n);
        for(int i = 0; i < n; i++) mat[i][i] = 1;
        return (mat);
    }
    
    Matrix &operator+=(const Matrix &B) {
        size_t n = height(), m = width();
        assert(n == B.height() && m == B.width());
        for(int i = 0; i < n; i++)
            for(int j = 0; j < m; j++)
                (*this)[i][j] += B[i][j];
        return (*this);
    }
    
    Matrix &operator-=(const Matrix &B) {
        size_t n = height(), m = width();
        assert(n == B.height() && m == B.width());
        for(int i = 0; i < n; i++)
            for(int j = 0; j < m; j++)
                (*this)[i][j] -= B[i][j];
        return (*this);
    }
    
    Matrix &operator*=(const Matrix &B) {
        size_t n = height(), m = B.width(), p = width();
        assert(p == B.height());
        vector< vector< T > > C(n, vector< T >(m, 0));
        for(int i = 0; i < n; i++)
            for(int j = 0; j < m; j++)
                for(int k = 0; k < p; k++)
                    C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
        A.swap(C);
        return (*this);
    }
    
    Matrix &operator^=(long long k) {
        Matrix B = Matrix::I(height());
        while(k > 0) {
            if(k & 1) B *= *this;
            *this *= *this;
            k >>= 1LL;
        }
        A.swap(B.A);
        return (*this);
    }
    
    Matrix operator+(const Matrix &B) const {
        return (Matrix(*this) += B);
    }
    
    Matrix operator-(const Matrix &B) const {
        return (Matrix(*this) -= B);
    }
    
    Matrix operator*(const Matrix &B) const {
        return (Matrix(*this) *= B);
    }
    
    Matrix operator^(const long long k) const {
        return (Matrix(*this) ^= k);
    }
    
    friend ostream &operator<<(ostream &os, Matrix &p) {
        size_t n = p.height(), m = p.width();
        for(int i = 0; i < n; i++) {
            os << "[";
            for(int j = 0; j < m; j++) {
                os << p[i][j] << (j + 1 == m ? "]\n" : ",");
            }
        }
        return (os);
    }
    
    
    T determinant() {
        Matrix B(*this);
        assert(width() == height());
        T ret = 1;
        for(int i = 0; i < width(); i++) {
            int idx = -1;
            for(int j = i; j < width(); j++) {
                if(B[j][i] != 0) idx = j;
            }
            if(idx == -1) return (0);
            if(i != idx) {
                ret *= -1;
                swap(B[i], B[idx]);
            }
            ret *= B[i][i];
            T vv = B[i][i];
            for(int j = 0; j < width(); j++) {
                B[i][j] /= vv;
            }
            for(int j = i + 1; j < width(); j++) {
                T a = B[j][i];
                for(int k = 0; k < width(); k++) {
                    B[j][k] -= B[i][k] * a;
                }
            }
        }
        return (ret);
    }
};

int main(){
    int M;
    lint K;
    cin >> M >> K;
    auto A = Matrix<modint>(M, M);
    rep(i, M){
        rep(j, M){
            int sum = (i + j) % M;
            A[i][sum] += 1;
            int mul = (i * j) % M;
            A[i][mul] += 1;
        }
    }
    auto x = Matrix<modint>(M, 1);
    x[0][0] = 1;
    A ^= K;
    x = A * x;
    cout << x[0][0] << endl;
}