#include using namespace atcoder; using mint = modint1000000007; // using mint = modint998244353; // using mint = modint;//mint::set_mod(MOD); const long long MOD = 1000000007; // const long long MOD = 998244353; #include #define rep(i, a, b) for (ll i = (ll)(a); i < (ll)(b); i++) #define repeq(i, a, b) for (ll i = (ll)(a); i <= (ll)(b); i++) #define repreq(i, a, b) for (ll i = (ll)(a); i >= (ll)(b); i--) #define each(a, b) for (auto &(a) : (b)) #define endl '\n' // fflush(stdout); #define cYes cout << "Yes" << endl #define cNo cout << "No" << endl #define sortr(v) sort(v, greater<>()) #define pb push_back #define mp make_pair #define mt make_tuple #define tget(a, b) get(a) #define FI first #define SE second #define ALL(v) (v).begin(), (v).end() #define INFLL 3000000000000000100LL #define INF 1000000100 #define PI acos(-1.0L) #define TAU (PI * 2.0L) using namespace std; typedef long long ll; typedef pair Pll; typedef tuple Tlll; typedef vector Vi; typedef vector VVi; typedef vector Vl; typedef vector VVl; typedef vector VVVl; typedef vector VTlll; typedef vector Vm; typedef vector VVm; typedef vector Vs; typedef vector Vd; typedef vector Vc; typedef vector Vb; typedef vector VPll; typedef priority_queue PQl; typedef priority_queue, greater> PQlr; /* print */ template ostream &operator<<(ostream &os, const vector &V) { int N = V.size(); if (N == 0) { os << endl; return os; } rep(i, 0, N - 1) { os << V[i] << ' '; } os << V[N - 1] << endl; return os; } template ostream &operator<<(ostream &os, const vector> &V) { int N = V.size(); rep(i, 0, N) os << V[i]; return os; } template ostream &operator<<(ostream &os, pair const &P) { os << P.FI << ' ' << P.SE; return os; } ostream &operator<<(ostream &os, mint const &M) { os << M.val(); return os; } /* useful */ template void Vin(vector &v) { int n = v.size(); rep(i, 0, n) cin >> v[i]; } template int SMALLER(vector &a, T x) { return lower_bound(a.begin(), a.end(), x) - a.begin(); } template int orSMALLER(vector &a, T x) { return upper_bound(a.begin(), a.end(), x) - a.begin(); } template int BIGGER(vector &a, T x) { return a.size() - orSMALLER(a, x); } template int orBIGGER(vector &a, T x) { return a.size() - SMALLER(a, x); } template int COUNT(vector &a, T x) { return upper_bound(ALL(a), x) - lower_bound(ALL(a), x); } template bool chmax(T &a, T b) { if (a < b) { a = b; return 1; } return 0; } template bool chmin(T &a, T b) { if (a > b) { a = b; return 1; } return 0; } template void press(T &v) { v.erase(unique(ALL(v)), v.end()); } template vector zip(vector b) { pair p[b.size() + 10]; int a = b.size(); vector l(a); for (int i = 0; i < a; i++) p[i] = mp(b[i], i); sort(p, p + a); int w = 0; for (int i = 0; i < a; i++) { if (i && p[i].first != p[i - 1].first) w++; l[p[i].second] = w; } return l; } template vector vis(vector &v) { vector S(v.size() + 1); rep(i, 1, S.size()) S[i] += v[i - 1] + S[i - 1]; return S; } ll dem(ll a, ll b) { return ((a + b - 1) / (b)); } ll dtoll(double d, int g) { return round(d * pow(10, g)); } const double EPS = 1e-10; void init() { cin.tie(0); cout.tie(0); ios::sync_with_stdio(0); cout << fixed << setprecision(12); } // Comm + K -> Comm + 0 // Comm + K -> Comm + C = add// // Comm + K -> Comm + U = del// /********************************** START **********************************/ template struct Matrix { vector> A; Matrix() {} Matrix(size_t n, size_t m) : A(n, vector(m, 0)) {} Matrix(size_t n) : A(n, vector(n, 0)){}; 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 mat(n); for (int i = 0; i < n; i++) mat[i][i] = 1; return (mat); } Matrix &operator+=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) (*this)[i][j] += B[i][j]; return (*this); } Matrix &operator-=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) (*this)[i][j] -= B[i][j]; return (*this); } Matrix &operator*=(const Matrix &B) { size_t n = height(), m = B.width(), p = width(); assert(p == B.height()); vector> C(n, vector(m, 0)); for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) for (int k = 0; k < p; k++) C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]); A.swap(C); return (*this); } Matrix &operator^=(long long k) { Matrix B = Matrix::I(height()); 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) { size_t n = p.height(), m = p.width(); for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) { os << p[i][j] << (j + 1 == m ? "\n" : " "); } } return (os); } T determinant() { // O(n^3) Matrix B(*this); assert(width() == height()); T ret = 1; for (int i = 0; i < width(); i++) { int idx = -1; for (int j = i; j < width(); j++) { if (B[j][i] != 0) idx = j; } if (idx == -1) return (0); if (i != idx) { ret *= -1; swap(B[i], B[idx]); } ret *= B[i][i]; T vv = B[i][i]; for (int j = 0; j < width(); j++) { B[i][j] /= vv; } for (int j = i + 1; j < width(); j++) { T a = B[j][i]; for (int k = 0; k < width(); k++) { B[j][k] -= B[i][k] * a; } } } return (ret); } }; vector> fact(long long n) { // 素因数分解O(√N) vector> r; for (ll i = 2; i * i <= n; ++i) { if (n % i) continue; r.emplace_back(i, 0); while (n % i == 0) { n /= i; r.back().second++; } } if (n != 1) r.emplace_back(n, 1); return r; } void sol() { ll n, m; cin >> n >> m; auto v = fact(m); mint ans = 1; auto f = [&](ll k) { Vm v(k + 1, 1); Matrix m(k + 1); rep(i, 0, k + 1) { repreq(j, k, k - i) { m[i][j] = 1; } } m ^= n - 1; mint ret = 0; rep(i, 0, k + 1) { mint ad = 0; rep(j, 0, k + 1) { ad += m[i][j] * v[j]; } ret += ad; } return ret; }; rep(i, 0, v.size()) { ans *= f(v[i].SE); } cout << ans << endl; } int main() { init(); int q = 1; // cin >> q; while (q--) sol(); return 0; }