【CF900D】Unusual Sequences

topic

Serious mental decline

Yeah obviously inversion

Must first meet \ (the X-| the y-\) , otherwise the answer is \ (0 \)

We enumerate the number of columns \ (gcd \) is \ (d \) or \ (d \) multiples

So the answer is,

\[\sum_{x|d}[d|y]\mu(\frac{x}{d})g(\frac{y}{d})\]

\ (g (d) \) shown and as \ (D \) Number of integers n columns, obviously plug lower plate, whereupon \ (g (d) = \ sum_ {i = 1} ^ d \ binom {d -1} {i-1} = 2 ^ {d-1} \)

Code

#include<bits/stdc++.h>
#define re register
#define LL long long
inline int read() {
    char c=getchar();int x=0;while(c<'0'||c>'9') c=getchar();
    while(c>='0'&&c<='9') x=(x<<3)+(x<<1)+c-48,c=getchar();return x;
}
const int mod=1e9+7;
const int maxn=1e5+5;
inline int ksm(int a,int b) {
    int S=1;
    for(;b;b>>=1,a=1ll*a*a%mod) if(b&1) S=1ll*S*a%mod;
    return S;
}
int n,m,T,ans;
int f[maxn],p[maxn>>1],mu[maxn];
inline int getmu(int x) {
    if(x<=T) return mu[x];int now=0;
    for(re int i=1;i<=p[0]&&x!=1;++i) {
        if(x%p[i]) continue;
        x/=p[i];now^=1;
        if(x%p[i]==0) return 0;
    }
    if(x!=1) now^=1;
    if(!now) return 1;return -1;
}
inline void add(int i) {
    if(i%n) return;
    int x=getmu(i/n);
    if(x==1) ans=(ans+ksm(2,m/i-1))%mod;
    if(x==-1) ans=(ans-ksm(2,m/i-1)+mod)%mod;
}
int main() {
    scanf("%d%d",&n,&m);
    if(m%n) {puts("0");return 0;}
    T=std::ceil(std::sqrt(m/n));f[1]=mu[1]=1;
    for(re int i=2;i<=T;i++) {
        if(!f[i]) p[++p[0]]=i,mu[i]=-1;
        for(re int j=1;j<=p[0]&&p[j]*i<=T;++j) {
            f[p[j]*i]=1;if(i%p[j]==0) break;
            mu[p[j]*i]=-1*mu[i];
        }
    }
    for(re int i=1;i*i<=m;++i) {
        if(m%i) continue;
        add(i);if(m/i!=i) add(m/i);
    }
    printf("%d\n",ans);
    return 0;
}