#include "bits/stdc++.h" using namespace std; using ll = long long; using pii = pair; using pll = pair; using vi = vector; using vl = vector; using vvi = vector; using vvl = vector; const ll INF = 1LL << 60; const ll MOD = 1000000007; template bool chmax(T &a, const T &b) { return (a < b) ? (a = b, 1) : 0; } template bool chmin(T &a, const T &b) { return (b < a) ? (a = b, 1) : 0; } template void print(const C &c, std::ostream &os = std::cout) { std::copy(std::begin(c), std::end(c), std::ostream_iterator(os, " ")); os << std::endl; } // list up all factors template set factors(T a) { set facs; for (T i = 1; i * i <= a; ++i) { if (a % i == 0) { facs.insert(i); facs.insert(a / i); } } return facs; } template void primeFactors(T a, map &facs) { double sqrtA = sqrt(a); for (int i = 2; i <= sqrtA + 1e-10; ++i) { while (a % i == 0) { facs[i]++; a /= i; } } if (a > sqrtA) facs[a]++; return; } // Eratosthenes's sieve // create list of prime numbers in O(N) // check if the given number is prime in O(1) struct Sieve { vector isPrime; Sieve(size_t max) : isPrime(max + 1, true) { isPrime[0] = false; isPrime[1] = false; for (size_t i = 2; i * i <= max; ++i) // 0からsqrt(max)まで調べる if (isPrime[i]) // iが素数ならば for (size_t j = 2; i * j <= max; ++j) // (max以下の)iの倍数は isPrime[i * j] = false; // 素数ではない } bool operator()(size_t n) { return isPrime[n]; } }; struct Combination { vector fac, finv, inv; Combination(ll maxN) { maxN += 100; // for safety fac.resize(maxN + 1); finv.resize(maxN + 1); inv.resize(maxN + 1); fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for (ll i = 2; i <= maxN; ++i) { fac[i] = fac[i - 1] * i % MOD; inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD; finv[i] = finv[i - 1] * inv[i] % MOD; } } ll operator()(ll n, ll k) { if (n < k) return 0; if (n < 0 || k < 0) return 0; return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD; } }; // mod int struct // original : https://github.com/beet-aizu/library/blob/master/mod/mint.cpp struct mint { ll v; ll mod; mint() : v(0) {} mint(signed v, ll mod = MOD) : v(v), mod(mod) {} mint(ll t, ll mod = MOD) : mod(mod) { v = t % mod; if (v < 0) v += mod; } mint pow(ll k) { mint res(1), tmp(v); while (k) { if (k & 1) res *= tmp; tmp *= tmp; k >>= 1; } return res; } static mint add_identity() { return mint(0); } static mint mul_identity() { return mint(1); } mint inv() { return pow(mod - 2); } mint &operator+=(mint a) { v += a.v; if (v >= mod) v -= mod; return *this; } mint &operator-=(mint a) { v += mod - a.v; if (v >= mod) v -= mod; return *this; } mint &operator*=(mint a) { v = 1LL * v * a.v % mod; return *this; } mint &operator/=(mint a) { return (*this) *= a.inv(); } mint operator+(mint a) const { return mint(v) += a; }; mint operator-(mint a) const { return mint(v) -= a; }; mint operator*(mint a) const { return mint(v) *= a; }; mint operator/(mint a) const { return mint(v) /= a; }; mint operator-() const { return v ? mint(mod - v) : mint(v); } bool operator==(const mint a) const { return v == a.v; } bool operator!=(const mint a) const { return v != a.v; } bool operator<(const mint a) const { return v < a.v; } // find x s.t. a^x = b static ll log(ll a, ll b) { const ll sq = 40000; unordered_map dp; dp.reserve(sq); mint res(1); for (int r = 0; r < sq; r++) { if (!dp.count(res.v)) dp[res.v] = r; res *= a; } mint p = mint(a).inv().pow(sq); res = b; for (int q = 0; q <= MOD / sq + 1; q++) { if (dp.count(res.v)) { ll idx = q * sq + dp[res.v]; if (idx > 0) return idx; } res *= p; } assert(0); return ll(-1); } static mint comb(long long n, int k) { mint num(1), dom(1); for (int i = 0; i < k; i++) { num *= mint(n - i); dom *= mint(i + 1); } return num / dom; } }; ostream &operator<<(ostream &os, mint m) { os << m.v; return os; } int main() { int n, k; cin >> n >> k; auto nfac = factors(n); auto kfac = factors(k); nfac.erase(1); kfac.erase(1); Sieve isprime(n); Combination nCk(n); mint ret = 0; for (auto &p : kfac) { if (nfac.count(p) > 0) { if (isprime(p)) { ret += mint(nCk(n / p, k / p)); } else { map primes; primeFactors(p, primes); bool con = false; for (auto &pp : primes) { if (pp.second >= 2) { con = true; break; } } if (con) continue; ret -= mint(nCk(n / p, k / p)) * mint(int(primes.size() % 2 == 0 ? 1 : -1)); } } } cout << ret << "\n"; return 0; }