#include using namespace std; typedef long long ll; typedef pair P; #define DUMP(x) cout << #x << " = " << (x) << endl; #define FOR(i, m, n) for (ll i = m; i < n; i++) #define IFOR(i, m, n) for (ll i = n - 1; i >= m; i--) #define REP(i, n) FOR(i, 0, n) #define IREP(i, n) IFOR(i, 0, n) #define FOREACH(x, a) for (auto&(x) : (a)) #define ALL(v) (v).begin(), (v).end() #define SZ(x) ll(x.size()) template struct Fp { long long val; constexpr Fp(long long v = 0) noexcept : val(v % MOD) { if (val < 0) val += MOD; } constexpr int getmod() { return MOD; } 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 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 ostream& operator<<(ostream& os, const Fp& x) noexcept { return os << x.val; } friend constexpr Fp modpow(const Fp& a, long long n) noexcept { if (n == 0) return 1; auto t = modpow(a, n / 2); t = t * t; if (n & 1) t = t * a; return t; } }; // 二項係数ライブラリ template struct BiCoef { vector fact_, inv_, finv_; constexpr BiCoef() {} constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) { init(n); } constexpr void init(int n) noexcept { fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1); int MOD = fact_[0].getmod(); for (int i = 2; i < n; i++) { fact_[i] = fact_[i - 1] * i; inv_[i] = -inv_[MOD % i] * (MOD / i); finv_[i] = finv_[i - 1] * inv_[i]; } } constexpr T com(int n, int k) const noexcept { if (n < k || n < 0 || k < 0) return 0; return fact_[n] * finv_[k] * finv_[n - k]; } constexpr T fact(int n) const noexcept { if (n < 0) return 0; return fact_[n]; } constexpr T inv(int n) const noexcept { if (n < 0) return 0; return inv_[n]; } constexpr T finv(int n) const noexcept { if (n < 0) return 0; return finv_[n]; } // C(n,k), n <= 1e9, k <= 1e6 constexpr T com2(int n, int k) const noexcept { if (n < k || n < 0 || k < 0) return 0; T res = 1; for (int i = n; i >= n - k + 1; i--) { T a = i, b = i - n + k; res *= a / b; } return res; } }; const int MOD = 1000000007; using mint = Fp; BiCoef bc; // 二項係数Library使用時はmain内で初期化を忘れないこと // int main(){ // bc.init(2100000); // } ll m, k; typedef vector> mat; mat matmul(const mat& A, const mat& B) { mat res(m, vector(m, 0)); REP(i, m) REP(j, m) REP(k, m) { res[i][j] += A[i][k] * B[k][j]; } return res; } mat matpow(mat& A, ll n) { if (n == 0) { mat res = mat(m, vector(m, 0)); REP(i, m) REP(j, m) { res[i][j] = 1; } return res; } if (n == 1) { return A; } if (n % 2 == 0) { mat B = matpow(A, n / 2); return matmul(B, B); } mat B = matpow(A, (n - 1) / 2); return matmul(matmul(B, B), A); } int main() { cin >> m >> k; vector> to(m, vector(m, 0)); REP(i, m) { REP(j, m) { to[i][(i + j) % m]++; to[i][(i * j) % m]++; } } mat to2(m, vector(m, 0)); REP(i, m) REP(j, m) { to2[i][j] = to[i][j]; } // REP(i, m) REP(j, m) { cout << to2[i][j] << " \n"[j == m - 1]; } mat B = matpow(to2, k); mint ans = B[0][0]; cout << ans << endl; }