#include #include typedef long long int ll; typedef long long int ull; #define MP make_pair using namespace std; using namespace atcoder; typedef pair P; // const ll MOD = 998244353; const ll MOD = 1000000007; // using mint = modint998244353; using mint = modint1000000007; const double pi = 3.1415926536; const int MAX = 2000003; long long fac[MAX], finv[MAX], inv[MAX]; template using min_priority_queue = priority_queue, greater>; void COMinit() { fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for (int i = 2; i < MAX; i++){ fac[i] = fac[i - 1] * i % MOD; inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD; finv[i] = finv[i - 1] * inv[i] % MOD; } } // 二項係数計算 long long COM(int n, int k){ if (n < k) return 0; if (n < 0 || k < 0) return 0; return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD; } ll gcd(ll x, ll y) { if (y == 0) return x; else if (y > x) { return gcd (y, x); } else return gcd(x % y, y); } ll lcm(ll x, ll y) { return x / gcd(x, y) * y; } ll my_sqrt(ll x) { ll m = 0; ll M = 3000000001; while (M - m > 1) { ll now = (M + m) / 2; if (now * now <= x) { m = now; } else { M = now; } } return m; } ll keta(ll n) { ll ret = 0; while (n) { n /= 10; ret++; } return ret; } ll ceil(ll n, ll m) { // n > 0, m > 0 ll ret = n / m; if (n % m) ret++; return ret; } ll pow_ll(ll x, ll n) { if (n == 0) return 1; if (n % 2) { return pow_ll(x, n - 1) * x; } else { ll tmp = pow_ll(x, n / 2); return tmp * tmp; } } template struct Matrix { using Array = array, H>; Array A; Matrix() : A() { for (int i = 0; i < H; i++) for (int j = 0; j < W; j++) (*this)[i][j] = T(); } int height() const { return H; } int width() const { return W; } inline const array &operator[](int k) const { return A[k]; } inline array &operator[](int k) { return A[k]; } static Matrix I() { assert(H == W); Matrix mat; for (int i = 0; i < H; i++) mat[i][i] = 1; return (mat); } Matrix &operator+=(const Matrix &B) { for (int i = 0; i < H; i++) for (int j = 0; j < W; j++) A[i][j] += B[i][j]; return (*this); } Matrix &operator-=(const Matrix &B) { for (int i = 0; i < H; i++) for (int j = 0; j < W; j++) A[i][j] -= B[i][j]; return (*this); } Matrix &operator*=(const Matrix &B) { assert(H == W); Matrix C; for (int i = 0; i < H; i++) for (int k = 0; k < H; k++) for (int j = 0; j < H; j++) C[i][j] += A[i][k] * B[k][j]; A.swap(C.A); return (*this); } Matrix &operator^=(long long k) { Matrix B = Matrix::I(); 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) { for (int i = 0; i < H; i++) { os << "["; for (int j = 0; j < W; j++) { os << p[i][j] << (j + 1 == W ? "]\n" : ","); } } return (os); } T determinant(int n = -1) { if (n == -1) n = H; Matrix B(*this); T ret = 1; for (int i = 0; i < n; i++) { int idx = -1; for (int j = i; j < n; j++) { if (B[j][i] != 0) { idx = j; break; } } if (idx == -1) return 0; if (i != idx) { ret *= T(-1); swap(B[i], B[idx]); } ret *= B[i][i]; T inv = T(1) / B[i][i]; for (int j = 0; j < n; j++) { B[i][j] *= inv; } for (int j = i + 1; j < n; j++) { T a = B[j][i]; if (a == 0) continue; for (int k = i; k < n; k++) { B[j][k] -= B[i][k] * a; } } } return (ret); } }; typedef Matrix matrix; matrix pow_mat(matrix a, ll n) { if (n == 0) { matrix x; return x.I(); } if (n % 2) { return a * pow_mat(a, n - 1); } else { matrix x = pow_mat(a, n / 2); return x * x; } } int main() { ll m, k; cin >> m >> k; matrix mat; for (int i = 0; i < m; i++) { for (int j = 0; j < m; j++) { mat[i][j] = 0; } } for (int i = 0; i < m; i++) { for (int j = 0; j < m; j++) { mat[i][(i + j) % m]++; mat[i][i * j % m]++; } } cout << pow_mat(mat, k)[0][0].val() << endl; return 0; }