#include using namespace std; #define REP(i, n) for (int i=0; i<(n); ++i) #define RREP(i, n) for (int i=(int)(n)-1; i>=0; --i) #define FOR(i, a, n) for (int i=(a); i<(n); ++i) #define RFOR(i, a, n) for (int i=(int)(n)-1; i>=(a); --i) #define SZ(x) ((int)(x).size()) #define ALL(x) (x).begin(),(x).end() #define DUMP(x) cerr<<#x<<" = "<<(x)< ostream &operator<<(ostream &os, const vector &v) { os << "["; REP(i, SZ(v)) { if (i) os << ", "; os << v[i]; } return os << "]"; } template ostream &operator<<(ostream &os, const pair &p) { return os << "(" << p.first << " " << p.second << ")"; } template bool chmax(T &a, const T &b) { if (a < b) { a = b; return true; } return false; } template bool chmin(T &a, const T &b) { if (b < a) { a = b; return true; } return false; } using ll = long long; using ull = unsigned long long; using ld = long double; using P = pair; using vi = vector; using vll = vector; using vvi = vector; using vvll = vector; const ll MOD = 1e9 + 7; const int INF = INT_MAX / 2; const ll LINF = LLONG_MAX / 2; const ld eps = 1e-9; template struct modint { using LL = int64_t; LL val; modint(LL val=0) : val(((val % mod) + mod) % mod) {} const modint operator+() const { return *this; } const modint operator-() const { return (-val + mod) % mod; } const modint inv() const { return pow(mod-2); } modint& operator+=(const modint& rhs) { (val += rhs.val) %= mod; return *this; } modint& operator-=(const modint& rhs) { return *this += -rhs; } modint& operator*=(const modint& rhs) { (val *= rhs.val) %= mod; return *this; } modint& operator/=(const modint& rhs) { return *this *= rhs.inv(); } const modint operator+(const modint& rhs) const { return modint(*this) += rhs; } const modint operator-(const modint& rhs) const { return modint(*this) -= rhs; } const modint operator*(const modint& rhs) const { return modint(*this) *= rhs; } const modint operator/(const modint& rhs) const { return modint(*this) /= rhs; } const modint pow(LL n) const { modint ret = 1, tmp = val; while (n) { if (n & 1) ret *= tmp; tmp *= tmp; n >>= 1; } return ret; } bool operator==(const modint& rhs) const { return val == rhs.val; } bool operator!=(const modint& rhs) const { return !(*this == rhs); } friend const modint operator+(const LL& lhs, const modint& rhs) { return modint(lhs) + rhs; } friend const modint operator-(const LL& lhs, const modint& rhs) { return modint(lhs) - rhs; } friend const modint operator*(const LL& lhs, const modint& rhs) { return modint(lhs) * rhs; } friend const modint operator/(const LL& lhs, const modint& rhs) { return modint(lhs) / rhs; } friend bool operator==(const LL& lhs, const modint& rhs) { return modint(lhs) == rhs; } friend bool operator!=(const LL& lhs, const modint& rhs) { return modint(lhs) != rhs; } friend ostream& operator<<(ostream& os, const modint& a) { return os << a.val; } friend istream& operator>>(istream& is, modint& a) { LL tmp; is >> tmp; a = tmp; return is; } }; template struct Matrix { vector> A; Matrix() {} Matrix(size_t n, size_t m) : A(n, vector(m)) {} Matrix(size_t n) : A(n, vector(n)) {}; size_t height() const { return (A.size()); } size_t width() const { return (A[0].size()); } inline const vector& operator[](int k) const { return (A.at(k)); } inline vector& operator[](int k) { return (A.at(k)); } static Matrix I(size_t n) { Matrix B(n); for (int i = 0; i < n; ++i) B[i][i] = 1; return (B); } Matrix operator-() const { size_t n = height(), m = width(); Matrix B = *this; for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) B[i][j] = -B[i][j]; return (B); } Matrix& operator+=(const Matrix& B) { size_t n = height(), m = width(); assert(n == B.height() and m == B.width()); for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) A[i][j] += B[i][j]; return (*this); } Matrix& operator-=(const Matrix& B) { return (*this += -B); } Matrix& operator*=(const Matrix& B) { size_t n = height(), m = B.width(), p = width(); assert(p == B.height()); Matrix C(n, m); for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) for (int k = 0; k < p; ++k) C[i][j] += A[i][k] * B[k][j]; A.swap(C.A); return (*this); } Matrix pow(int64_t k) { Matrix B = Matrix::I(height()), tmp = *this; while (k) { if (k & 1) B *= tmp; tmp *= tmp; k >>= 1; } return (B); } const Matrix operator+(const Matrix& B) const { return (Matrix(*this) += B); } const Matrix operator-(const Matrix& B) const { return (Matrix(*this) -= B); } const Matrix operator*(const Matrix& B) const { return (Matrix(*this) *= B); } int GaussJordanElimination() { int rank = 0; for (int col = 0; col < width(); ++col) { int pivot = -1; for (int row = rank; row < height(); ++row) { if (A[row][col] != 0) { pivot = row; break; } } if (pivot == -1) continue; swap(A[rank], A[pivot]); T topLeft = A[rank][col]; for (int c = col; c < width(); ++c) { A[rank][c] /= topLeft; } for (int row = rank+1; row < height(); ++row) { T ratio = A[row][col]; for (int c = col; c < width(); ++c) A[row][c] -= ratio * A[rank][c]; } ++rank; } return (rank); } friend istream& operator>>(istream& is, Matrix& B) { is >> B.A; return (is); } friend ostream& operator<<(ostream& os, Matrix& B) { size_t n = B.height(), m = B.width(); for (int i = 0; i < n; ++i) { os << (i == 0 ? "[" : " "); for (int j = 0; j < m; ++j) { os << B[i][j] << (j == m-1 ? "]" : ","); } os << (i == n-1 ? "]\n" : ",\n"); } return (os); } }; int main() { cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(10); // ifstream in("in.txt"); // cin.rdbuf(in.rdbuf()); ll M, K; cin >> M >> K; using Int = modint; Matrix A(M, M); REP(i, M) { REP(j, M) { A[i][(i + j) % M] += 1; A[i][(i * j) % M] += 1; } } Matrix p(1, M); p[0][0] = 1; p = p * A.pow(K); cout << p[0][0] << endl; return 0; }