#include #include using namespace std; using namespace atcoder; using ll = long long; using mint = modint1000000007; template struct Matrix : vector> { using vector>::vector; using vector>::operator=; Matrix() {} Matrix(ll n) { this->assign(n, vector(n, 0)); for(ll i = 0; i < n; i++) { (*this)[i][i] = 1; } } Matrix(ll n, ll m, T x = 0) { for(ll i = 0; i < n; i++) { this->push_back(vector(m, x)); } } Matrix(vector> v) { *this = v; } Matrix operator+(const Matrix &m) const { return Matrix(*this) += m; } Matrix operator-(const Matrix &m) const { return Matrix(*this) -= m; } Matrix operator*(const Matrix &m) const { return Matrix(*this) *= m; } Matrix operator*(const T &x) const { return Matrix(*this) *= x; } Matrix operator^(ll n) const { return Matrix(*this) ^= n; } Matrix operator+=(const Matrix &m) const { ll h = this->size(), w = (*this)[0].size(); assert(h == m.size() && w == m[0].size()); for(ll i = 0; i < h; i++) { for(ll j = 0; j < w; j++) { *this[i][j] += m[i][j]; } } return *this; } Matrix operator-=(const Matrix &m) { ll h = this->size(), w = (*this)[0].size(); assert(h == m.size() && w == m[0].size()); for(ll i = 0; i < h; i++) { for(ll j = 0; j < w; j++) { *this[i][j] -= m[i][j]; } } return *this; } Matrix operator*=(const Matrix &m) { ll h = this->size(), w = (*this)[0].size(); assert(w == (ll)m.size()); vector> r(h, vector(m[0].size(), T(0))); for(ll i = 0; i < h; i++) { for(ll j = 0; j < (ll)m[0].size(); j++) { for(ll k = 0; k < w; k++) { r[i][j] += (*this)[i][k] * m[k][j]; } } } this->swap(r); return *this; } Matrix operator*=(const T &x) { ll h = this->size(), w = (*this)[0].size(); for(ll i = 0; i < h; i++) { for(ll j = 0; j < w; j++) { *this[i][j] *= x; } } return *this; } Matrix operator^=(ll n) { ll h = this->size(); Matrix m(h); while(n) { if(n & 1) { m *= *this; } *this *= *this; n >>= 1LL; } this->swap(m); return *this; } }; int main() { ios::sync_with_stdio(false); cin.tie(nullptr); ll N, K; cin >> N >> K; Matrix dp(N, 1), m(N, N); dp[0][0] = 1; for(ll i = 0; i < N; i++) { for(ll j = 0; j < N; j++) { m[(i + j) % N][i]++; m[i * j % N][i]++; } } dp = (m ^ K) * dp; cout << dp[0][0].val() << "\n"; }