#include #define LLI long long int #define FOR(v, a, b) for(LLI v = (a); v < (b); ++v) #define FORE(v, a, b) for(LLI v = (a); v <= (b); ++v) #define REP(v, n) FOR(v, 0, n) #define REPE(v, n) FORE(v, 0, n) #define REV(v, a, b) for(LLI v = (a); v >= (b); --v) #define ALL(x) (x).begin(), (x).end() #define RALL(x) (x).rbegin(), (x).rend() #define ITR(it, c) for(auto it = (c).begin(); it != (c).end(); ++it) #define RITR(it, c) for(auto it = (c).rbegin(); it != (c).rend(); ++it) #define EXIST(c,x) ((c).find(x) != (c).end()) #define fst first #define snd second #define popcount __builtin_popcount #define UNIQ(v) (v).erase(unique(ALL(v)), (v).end()) #define bit(i) (1LL<<(i)) #ifdef DEBUG #include #else #define dump(...) ((void)0) #endif #define gcd __gcd using namespace std; template constexpr T lcm(T m, T n){return m/gcd(m,n)*n;} template void join(ostream &ost, I s, I t, string d=" "){for(auto i=s; i!=t; ++i){if(i!=s)ost< istream& operator>>(istream &is, vector &v){for(auto &a : v) is >> a; return is;} template bool chmin(T &a, const U &b){return (a>b ? a=b, true : false);} template bool chmax(T &a, const U &b){return (a void fill_array(T (&a)[N], const U &v){fill((U*)a, (U*)(a+N), v);} struct Init{ Init(){ cin.tie(0); ios::sync_with_stdio(false); } }init; template class ModInt{ public: uint64_t val; ModInt(): val(0){} ModInt(int64_t n){ if(n >= M) val = n % M; else if(n < 0) val = n % M + M; else val = n; } inline constexpr ModInt operator+(const ModInt &a) const {return ModInt((val+a.val)%M);} inline constexpr ModInt operator-(const ModInt &a) const {return ModInt((val-a.val+M)%M);} inline constexpr ModInt operator*(const ModInt &a) const {return ModInt((val*a.val)%M);} inline constexpr ModInt operator/(const ModInt &a) const {return ModInt((val*a.inv().val)%M);} inline constexpr ModInt& operator=(const ModInt &a){val = a.val; return *this;} inline constexpr ModInt& operator+=(const ModInt &a){if((val += a.val) >= M) val -= M; return *this;} inline constexpr ModInt& operator-=(const ModInt &a){if(val < a.val) val += M; val -= a.val; return *this;} inline constexpr ModInt& operator*=(const ModInt &a){(val *= a.val) %= M; return *this;} inline constexpr ModInt& operator/=(const ModInt &a){(val *= a.inv().val) %= M; return *this;} inline constexpr bool operator==(const ModInt &a) const {return val==a.val;} inline constexpr bool operator!=(const ModInt &a) const {return val!=a.val;} inline constexpr ModInt& operator++(){*this += 1; return *this;} inline constexpr ModInt& operator--(){*this -= 1; return *this;} inline constexpr ModInt operator++(int){ModInt t = *this; *this += 1; return t;} inline constexpr ModInt operator--(int){ModInt t = *this; *this -= 1; return t;} inline constexpr static ModInt power(LLI n, LLI p){ ModInt ret = 1, e = n; for(; p; e *= e, p >>= 1) if(p&1) ret *= e; return ret; } inline constexpr ModInt power(LLI p) const {return power(val,p);} inline constexpr ModInt inv() const { int64_t a = val, b = M, u = 1, v = 0; while(b){ int64_t t = a/b; a -= t*b; swap(a,b); u -= t*v; swap(u,v); } u %= M; if(u < 0) u += M; return u; } }; template ModInt operator-(const ModInt &a){return M-a.val;} template ModInt operator+(int64_t a, const ModInt &b){return ModInt(ModInt(a)+b.val);} template ModInt operator-(int64_t a, const ModInt &b){return ModInt(ModInt(a)-b.val);} template ModInt operator*(int64_t a, const ModInt &b){return ModInt(ModInt(a)*b.val);} template ModInt operator/(int64_t a, const ModInt &b){return ModInt(ModInt(a)/b.val);} template istream& operator>>(istream &is, ModInt &a){is >> a.val; return is;} template ostream& operator<<(ostream &os, const ModInt &a){ os << a.val; return os;} using mint = ModInt<1000000007>; /** * @attention 使用前にinit関数を呼び出す */ template class CombUtilsMint{ public: static vector facto; static vector ifacto; static void init(int N){ facto.assign(N+1, 1); ifacto.assign(N+1, 1); FORE(i,1,N){ facto[i] = facto[i-1] * i; } ifacto[N] = facto[N].inv(); REV(i,N-1,0){ ifacto[i] = ifacto[i+1] * (i+1); } } static T f(LLI i){ assert(i < facto.size()); return facto[i]; } static T finv(LLI i){ assert(i < ifacto.size()); return ifacto[i]; } static T P(LLI n, LLI k); static T C(LLI n, LLI k); static T H(LLI n, LLI k); static T stirling_number(LLI n, LLI k); static T bell_number(LLI n, LLI k); static vector bernoulli_number(LLI n); }; template vector CombUtilsMint::facto = vector(); template vector CombUtilsMint::ifacto = vector(); template T CombUtilsMint::P(LLI n, LLI k){ if(n < k or n < 0 or k < 0) return 0; return f(n) * finv(n-k); } template T CombUtilsMint::C(LLI n, LLI k){ if(n < k or n < 0 or k < 0) return 0; return P(n,k) * finv(k); } template T CombUtilsMint::H(LLI n, LLI k){ if(n == 0 and k == 0) return 1; return C(n+k-1, k); } vector eratosthenes_sieve(int n){ vector res(n+1, true); res[0] = res[1] = false; FOR(i,2,n) if(res[i]) for(int j=2*i; j<=n; j+=i) res[j] = false; return res; } auto is_prime = eratosthenes_sieve(1000000); /** * @details * mu(1) = 1 * * mu(n) = 0 if nが平方因子を持つ * * mu(n) = (-1)^k if nが相異なるk個の素因数に分解される * * mu(nm) = mu(n) * mu(m) if nとmが互いに素 */ vector mobius(int n){ vector ret(n+1); vector ps; ret[1] = 1; FORE(i,2,n){ if(is_prime[i]){ ps.push_back(i); ret[i] = -1; } for(auto &j : ps){ if(i*j > n) break; if(i%j == 0) ret[i*j] = 0; else ret[i*j] = ret[i] * ret[j]; } } return ret; } using C = CombUtilsMint; int main(){ C::init(1000000); auto m = mobius(1000000); int N,K; while(cin >> N >> K){ vector f(N+1); FOR(i,1,N){ if(N % i == 0){ int d = N/i; if(K % d == 0){ f[i] = C::C(i,K/d); } } } mint ans = 0; FOR(i,1,N){ if(N % i != 0) continue; FORE(j,1,i){ if(i % j == 0){ ans += m[i/j] * f[j]; } } } cout << ans << endl; } return 0; }