#pragma GCC optimize ("Ofast") #include using namespace std; #define MD 1000000007 void *wmem; char memarr[96000000]; template inline void walloc1d(T **arr, int x, void **mem = &wmem){ static int skip[16] = {0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}; (*mem) = (void*)( ((char*)(*mem)) + skip[((unsigned long long)(*mem)) & 15] ); (*arr)=(T*)(*mem); (*mem)=((*arr)+x); } struct mint{ static unsigned md; static unsigned W; static unsigned R; static unsigned Rinv; static unsigned mdninv; static unsigned RR; unsigned val; mint(){ } mint(int a){ val = mulR(a); } mint(unsigned a){ val = mulR(a); } mint(long long a){ val = mulR(a); } mint(unsigned long long a){ val = mulR(a); } int get_inv(long long a, int md){ long long t=a; long long s=md; long long u=1; long long v=0; long long e; while(s){ e=t/s; t-=e*s; u-=e*v; swap(t,s); swap(u,v); } if(u<0){ u+=md; } return u; } void setmod(unsigned m){ int i; unsigned t; W = 32; md = m; R = (1ULL << W) % md; RR = (unsigned long long)R*R % md; switch(m){ case 104857601: Rinv = 2560000; mdninv = 104857599; break; case 998244353: Rinv = 232013824; mdninv = 998244351; break; case 1000000007: Rinv = 518424770; mdninv = 2226617417U; break; case 1000000009: Rinv = 171601999; mdninv = 737024967; break; case 1004535809: Rinv = 234947584; mdninv = 1004535807; break; case 1007681537: Rinv = 236421376; mdninv = 1007681535; break; case 1012924417: Rinv = 238887936; mdninv = 1012924415; break; case 1045430273: Rinv = 254466304; mdninv = 1045430271; break; case 1051721729: Rinv = 257538304; mdninv = 1051721727; break; default: Rinv = get_inv(R, md); mdninv = 0; t = 0; for(i=(0);i<((int)W);i++){ if(t%2==0){ t+=md; mdninv |= (1U<> W); if(t >= md){ t -= md; } return t; } unsigned reduce(unsigned long long T){ unsigned m = (unsigned)T * mdninv; unsigned t = (unsigned)((T + (unsigned long long)m*md) >> W); if(t >= md){ t -= md; } return t; } unsigned get(){ return reduce(val); } mint &operator+=(mint a){ val += a.val; if(val >= md){ val -= md; } return *this; } mint &operator-=(mint a){ if(val < a.val){ val = val + md - a.val; } else{ val -= a.val; } return *this; } mint &operator*=(mint a){ val = reduce((unsigned long long)val*a.val); return *this; } mint &operator/=(mint a){ return *this *= a.inverse(); } mint operator+(mint a){ return mint(*this)+=a; } mint operator-(mint a){ return mint(*this)-=a; } mint operator*(mint a){ return mint(*this)*=a; } mint operator/(mint a){ return mint(*this)/=a; } mint operator+(int a){ return mint(*this)+=mint(a); } mint operator-(int a){ return mint(*this)-=mint(a); } mint operator*(int a){ return mint(*this)*=mint(a); } mint operator/(int a){ return mint(*this)/=mint(a); } mint operator+(long long a){ return mint(*this)+=mint(a); } mint operator-(long long a){ return mint(*this)-=mint(a); } mint operator*(long long a){ return mint(*this)*=mint(a); } mint operator/(long long a){ return mint(*this)/=mint(a); } mint operator-(void){ mint res; if(val){ res.val=md-val; } else{ res.val=0; } return res; } operator bool(void){ return val!=0; } operator int(void){ return get(); } operator long long(void){ return get(); } mint inverse(){ int a = val; int b = md; int u = 1; int v = 0; int t; mint res; while(b){ t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } if(u < 0){ u += md; } res.val = (unsigned long long)u*RR % md; return res; } mint pw(unsigned long long b){ mint a(*this); mint res; res.val = R; while(b){ if(b&1){ res *= a; } b >>= 1; a *= a; } return res; } bool operator==(int a){ return mulR(a)==val; } bool operator!=(int a){ return mulR(a)!=val; } } ; unsigned mint::md; unsigned mint::W; unsigned mint::R; unsigned mint::Rinv; unsigned mint::mdninv; unsigned mint::RR; mint operator+(int a, mint b){ return mint(a)+=b; } mint operator-(int a, mint b){ return mint(a)-=b; } mint operator*(int a, mint b){ return mint(a)*=b; } mint operator/(int a, mint b){ return mint(a)/=b; } mint operator+(long long a, mint b){ return mint(a)+=b; } mint operator-(long long a, mint b){ return mint(a)-=b; } mint operator*(long long a, mint b){ return mint(a)*=b; } mint operator/(long long a, mint b){ return mint(a)/=b; } inline void rd(int &x){ int k; int m=0; x=0; for(;;){ k = getchar_unlocked(); if(k=='-'){ m=1; break; } if('0'<=k&&k<='9'){ x=k-'0'; break; } } for(;;){ k = getchar_unlocked(); if(k<'0'||k>'9'){ break; } x=x*10+k-'0'; } if(m){ x=-x; } } inline void wt_L(char a){ putchar_unlocked(a); } inline void wt_L(int x){ int s=0; int m=0; char f[10]; if(x<0){ m=1; x=-x; } while(x){ f[s++]=x%10; x/=10; } if(!s){ f[s++]=0; } if(m){ putchar_unlocked('-'); } while(s--){ putchar_unlocked(f[s]+'0'); } } inline void wt_L(mint x){ int i; i = (int)x; wt_L(i); } template int Factor_L(T N, T fac[], int fs[]){ T i; int sz = 0; if(N%2==0){ fac[sz] = 2; fs[sz] = 1; N /= 2; while(N%2==0){ N /= 2; fs[sz]++; } sz++; } for(i=3;i*i<=N;i+=2){ if(N%i==0){ fac[sz] = i; fs[sz] = 1; N /= i; while(N%i==0){ N /= i; fs[sz]++; } sz++; } } if(N > 1){ fac[sz] = N; fs[sz] = 1; sz++; } return sz; } template int Divisor_L(T N, T res[], void *mem = wmem){ int i; int j; int k; int s; int sz = 0; T *fc; int *fs; int fsz; walloc1d(&fc, 100, &mem); walloc1d(&fs, 100, &mem); fsz =Factor_L(N, fc, fs); res[sz++] = 1; for(i=(0);i<(fsz);i++){ s = sz; k = s * fs[i]; for(j=(0);j<(k);j++){ res[sz++] = res[j] * fc[i]; } } sort(res, res+sz); return sz; } template int Moebius_L(T n){ T i; int res = 1; if(n%4==0){ return 0; } if(n%2==0){ n /= 2; res = -res; } for(i=3;i*i<=n;i+=2){ if(n%i==0){ n /= i; res = -res; } if(n%i==0){ return 0; } } if(n > 1){ res = -res; } return res; } template inline T GCD_L(T a,T b){ T r; while(a){ r=b; b=a; a=r%a; } return b; } struct combination_mint{ mint *fac; mint *ifac; void init(int n, void **mem = &wmem){ int i; walloc1d(&fac, n, mem); walloc1d(&ifac, n, mem); fac[0] = 1; for(i=(1);i<(n);i++){ fac[i] = fac[i-1] * i; } ifac[n-1] = 1 / fac[n-1]; for(i=n-2;i>=0;i--){ ifac[i] = ifac[i+1] * (i+1); } } mint C(int a, int b){ if(b < 0 || b > a){ return 0; } return fac[a]*ifac[b]*ifac[a-b]; } mint P(int a, int b){ if(b < 0 || b > a){ return 0; } return fac[a]*ifac[a-b]; } mint H(int a, int b){ if(a==0 && b==0){ return 1; } if(a<=0 || b<0){ return 0; } return C(a+b-1, b); } } ; int ys; int y[10000]; int main(){ int i; wmem = memarr; { mint x; x.setmod(MD); } int N; int K; mint res; combination_mint c; rd(N); rd(K); c.init(N+1); res = 0; ys =Divisor_L(GCD_L(N, K),y); for(i=(1);i<(ys);i++){ res -=Moebius_L(y[i])* c.C(N/y[i], K/y[i]); } wt_L(res); wt_L('\n'); return 0; } // cLay varsion 20190921-1 // --- original code --- // int ys, y[1d4]; // { // int N, K; // mint res; // combination_mint c; // // rd(N,K); // c.init(N+1); // // res = 0; // ys = Divisor(gcd(N,K),y); // rep(i,1,ys) res -= Moebius(y[i]) * c.C(N/y[i], K/y[i]); // wt(res); // }