Submission #9134

#TimeUsernameProblemLanguageResultExecution timeMemory
9134imsifileActual visible points (kriii2_AC)C++98
4 / 4
220 ms7336 KiB
#include<stdio.h>
#define mod 1000000007

typedef long long lld;

int n, m, mx, ba[200000];
lld fac[300000], soin[200000], real[200000], dap;

lld exp(lld x, lld y){
	if(y==0)return 1;
	lld im=exp(x,y/2);
	im=(im*im)%mod;
	if(y%2)im=(im*x)%mod;
	return im;
}

lld comb(lld a, lld b){
	lld im=fac[a-b]*fac[b]%mod;
	return fac[a]*exp(im,mod-2)%mod;
}

int main(){
	int i, j, a;
	scanf("%d%d", &n, &m);
	fac[0]=1;
	for(i=1; i<300000; i++)fac[i]=fac[i-1]*i%mod;
	for(i=0; i<m; i++){
		scanf("%d", &a);
		if(mx<a)mx=a;
		ba[a]=1;
	}
	for(i=1; i<=mx; i++){
		if(ba[i])continue;
		for(a=i*2; a<=mx; a+=i){
			if(ba[a])break;
		}
		if(a<=mx)ba[i]=1;
	}
	soin[1]=1;
	for(i=2; i<=mx; i++){
		for(a=2; a*a<=i; a++){
			if(i%a==0)break;
		}
		if(a*a>i)soin[i]=-1;
		else if(i%(a*a)==0)soin[i]=0;
		else soin[i]=soin[i/a]*soin[a];
	}
	for(i=1; i<=mx; i++){
		if(!ba[i])continue;
		for(a=1; a*a<=i; a++){
			if(i%a==0){
				real[i/a]+=soin[a];
				if(a*a<i)real[a]+=soin[i/a];
			}
		}
	}
	for(i=1; i<=mx; i++){
		dap+=real[i]*comb(i+n-2, n-1);
		dap=(dap+mod)%mod;
	}
	printf("%lld", dap);
	return 0;
}
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