#include #include using namespace atcoder; #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #define rep(i, n) for(ll i = 0; i < n; i++) #define rep2(i, m, n) for(ll i = m; i <= n; i++) #define rrep(i, m, n) for(ll i = m; i >= n; i--) #define all(a) a.begin(), a.end() #define rall(a) a.rbegin(), a.rend() #define MAX(x) *max_element(all(x)) #define MIN(x) *min_element(all(x)) #define SZ(a) ((ll)(a).size()) #define bit(n, k) ((n >> k) & 1) using namespace std; using ll = long long; using P = pair; const int dx[4] = { 1, 0, -1, 0}; const int dy[4] = { 0, -1, 0, 1}; const int inf = 1e9 + 1; const ll infll = 1e18; //const double pi = acos(-1); using Graph = vector>; using REV_PQ = priority_queue, greater>; using PQ = priority_queue; const int SIZE = 400010; ll powll(ll n, ll x) { // return n ^ x; ll ret = 1; rep(i, x) ret *= n; return ret; } void OutputYesNo(bool val) { if (val) cout << "Yes" << endl; else cout << "No" << endl; } void OutputTakahashiAoki(bool val) { if (val) cout << "Takahashi" << endl; else cout << "Aoki" << endl; } void OutPutInteger(ll x) { cout << x << endl; } void OutPutString(string x) { cout << x << endl; } int pop_count(ll n){ int ret = 0; while(n > 0){ if(n % 2 == 1) ret++; n /= 2; } return ret; } //using PAIR_REV_PQ = priority_queue, vector>, greater>>; //typedef atcoder::modint998244353 mint; //typedef atcoder::modint1000000007 mint; //typedef modint mint; //typedef vector ModintVec; //typedef vector ModintMat; const int MAX_N = 100100; vector prime; // i.th prime vector first_prime(MAX_N + 1); // その数を最初に割り切る素数を格納 i = first_prime[i]ならiは素数(i≧2) void sieve() { for (int i = 0; i <= MAX_N; i++) first_prime[i] = 1; first_prime[0] = first_prime[1] = 1; for (int i = 2; i <= MAX_N; i++) { if (first_prime[i] == 1) { prime.push_back(i); for (int j = i; j <= MAX_N; j += i) first_prime[j] = i; } } } int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); int n, p; cin >> n >> p; sieve(); int cnt = 0; rep2(i, 1, n){ int j = i; while(j > 1){ int x = first_prime[j]; while(first_prime[j] == x){ if(x == p) cnt++; j /= x; } } } using mint1 = dynamic_modint<0>; mint1::set_mod(1000000007); using mint2 = dynamic_modint<1>; mint2::set_mod(1000000006); mint1 res = cnt; mint2 x_m_1 = 1; mint1 x_m = 1; rep2(i, 1, n){ x_m *= i; x_m_1 *= i; } res *= mint1(x_m.val()).pow(x_m_1.val()); cout << res.val() << endl; }