#include using namespace std; using ll = long long; using pii = pair; template using V = vector; template using VV = V>; #define pb push_back #define eb emplace_back #define mp make_pair #define fi first #define se second #define rep(i, n) rep2(i, 0, n) #define rep2(i, m, n) for (int i = m; i < (n); i++) #define ALL(c) (c).begin(), (c).end() constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); } template void chmin(T& t, const U& u) { if (t > u) t = u; } template void chmax(T& t, const U& u) { if (t < u) t = u; } template ostream& operator<<(ostream& os, const pair& p) { os << "(" << p.first << "," << p.second << ")"; return os; } template ostream& operator<<(ostream& os, const vector& v) { os << "{"; rep(i, v.size()) { if (i) os << ","; os << v[i]; } os << "}"; return os; } #ifdef LOCAL void debug_out() { cerr << endl; } template void debug_out(Head H, Tail... T) { cerr << " " << H; debug_out(T...); } #define debug(...) \ cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__) #define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl #else #define debug(...) (void(0)) #define dump(x) (void(0)) #endif template struct ModInt { using uint = unsigned int; using ull = unsigned long long; using M = ModInt; uint v; ModInt(ll _v = 0) { set_norm(_v % MOD + MOD); } M& set_norm(uint _v) { //[0, MOD * 2)->[0, MOD) v = (_v < MOD) ? _v : _v - MOD; return *this; } explicit operator bool() const { return v != 0; } M operator+(const M& a) const { return M().set_norm(v + a.v); } M operator-(const M& a) const { return M().set_norm(v + MOD - a.v); } M operator*(const M& a) const { return M().set_norm(ull(v) * a.v % MOD); } M operator/(const M& a) const { return *this * a.inv(); } M& operator+=(const M& a) { return *this = *this + a; } M& operator-=(const M& a) { return *this = *this - a; } M& operator*=(const M& a) { return *this = *this * a; } M& operator/=(const M& a) { return *this = *this / a; } M operator-() const { return M() - *this; } M& operator++(int) { return *this = *this + 1; } M& operator--(int) { return *this = *this - 1; } M pow(ll n) const { if (n < 0) return inv().pow(-n); M x = *this, res = 1; while (n) { if (n & 1) res *= x; x *= x; n >>= 1; } return res; } M inv() const { ll a = v, b = MOD, p = 1, q = 0, t; while (b != 0) { t = a / b; swap(a -= t * b, b); swap(p -= t * q, q); } return M(p); } bool operator==(const M& a) const { return v == a.v; } bool operator!=(const M& a) const { return v != a.v; } friend ostream& operator<<(ostream& os, const M& a) { return os << a.v; } static uint get_mod() { return MOD; } }; using Mint = ModInt<1000000007>; const Mint zero(0); const Mint one(1); bool iszero(Mint x) { return x.v == 0; } bool isone(Mint x) { return x.v == 1; } template struct Matrix { int H, W; VV a; Matrix() : H(0), W(0) {} Matrix(int H, int W) : H(H), W(W), a(VV(H, V(W))) {} Matrix(const VV& v) : H(v.size()), W(v[0].size()), a(v) {} static Matrix E(int n) { Matrix a(n, n); rep(i, n) a.set(i, i, 1); return a; } T at(int i, int j) const { return a[i][j]; } void set(int i, int j, T v) { a[i][j] = v; } Matrix operator+(const Matrix& r) const { assert(H == r.H && W == r.W); VV v(H, V(W)); rep(i, H) rep(j, W) v[i][j] = a[i][j] + r.a[i][j]; return Matrix(v); } Matrix operator-(const Matrix& r) const { assert(H == r.H && W == r.W); VV v(H, V(W)); rep(i, H) rep(j, W) v[i][j] = a[i][j] - r.a[i][j]; return Matrix(v); } Matrix operator*(const Matrix& r) const { assert(W == r.H); VV v(H, V(r.W)); rep(i, H) rep(k, W) rep(j, r.W) v[i][j] += a[i][k] * r.a[k][j]; return Matrix(v); } Matrix& operator+=(const Matrix& r) { return (*this) = (*this) + r; } Matrix& operator-=(const Matrix& r) { return (*this) = (*this) - r; } Matrix& operator*=(const Matrix& r) { return (*this) = (*this) * r; } /* 副作⽤がある, 基本的に⾃分でこれを呼ぶことはない 掃き出し法をする 左からvar列が掃き出す対象で、それより右は同時に値を変更するだけ(e.g. 逆⾏列 は右に単位⾏列おいてから掃き出す) ⾏swap, 列swap は⾏わない rank を返す */ int sweep(int var) { int rank = 0; vector used(H); rep(j, var) { int i = 0; while (i < H && (used[i] || iszero(a[i][j]))) i++; if (i == H) continue; used[i] = true; rank++; T t = a[i][j]; rep(k, W) a[i][k] = a[i][k] / t; rep(k, H) if (k != i) { T t = a[k][j]; rep(l, W) a[k][l] = a[k][l] - a[i][l] * t; } } return rank; } Matrix pow(ll n) const { assert(H == W); int h = H; Matrix x = *this, res(h, h); res = E(h); while (n > 0) { if (n & 1) res *= x; x *= x; n >>= 1; } return res; } friend ostream& operator<<(ostream& o, const Matrix& A) { rep(i, A.H) { rep(j, A.W) o << A.a[i][j] << " "; o << endl; } return o; } }; int main() { int M, K; cin >> M >> K; Matrix mat(M, M); rep(i, M) { rep(j, M) { mat.a[i][(i + j) % M]++; mat.a[i][(i * j) % M]++; } } auto mt = mat.pow(K); Mint ans = mt.a[0][0]; cout << ans << endl; return 0; }