OJ-Problems-Source/HDOJ/5201_autoAC.cpp

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#include<stdio.h>
typedef long long LL;
#define mod 1000000007
LL pow(LL a, LL b) {
LL s = 1;
while(b) {
if(b&1) s = (s * a) % mod;
a = (a*a) % mod;
b >>= 1;
}
return s;
}
LL f[200005],inv[200005];
void init()
{
f[0]=f[1]=inv[0]=inv[1]=1;
for(LL i=2;i<=200000;++i){
f[i]=f[i-1]*i%mod;
inv[i]=pow(f[i],mod-2);
}
}
LL C(int n,int m)
{
if(m>n||m<0) return 0;
return f[n]*inv[m]%mod*inv[n-m]%mod;
}
LL n,m;
LL cal(int x)
{
LL ans=0;
for(LL i=0,s=x;i<m&&s<=n;++i,s+=x)
{
LL t=C(m-1,i)*C(n-s+m-2,n-s)%mod;
if(i&1) ans=((ans-t)%mod+mod)%mod;
else ans=(ans+t)%mod;
}
return ans;
}
int main() {
int t;
scanf("%d",&t);
init();
while(t--)
{
scanf("%lld%lld", &n,&m);
if(m==1) puts("1");
else
{
LL ans=0;
for(LL i=1;i<=n;++i) ans=(ans+cal(i))%mod;
printf("%lld\n",ans);
}
}
return 0;
}