OJ-Problems-Source/HDOJ/4732_autoAC.cpp
2016-09-10 11:31:03 +08:00

125 lines
3.0 KiB
C++

#include <set>
#include <map>
#include <vector>
#include <algorithm>
#include <cstdio>
#include <iostream>
using namespace std;
typedef long long LL;
typedef pair<int,int> PII;
#define MP make_pair
#define PB push_back
#define AA first
#define BB second
#define OP begin()
#define ED end()
#define SZ size()
#define cmin(x,y) x=min(x,y)
#define cmax(x,y) x=max(x,y)
const LL MOD = 1000000007;
const int MXN = 200005;
int mu[MXN], p[MXN], pn;
bool flag[MXN];
void init(int n=MXN-5) {
pn = 0;
mu[1] = 1;
for(int i = 2; i <= n; i++) {
if(!flag[i]) {
p[pn ++ ] = i;
mu[i] = -1;
}
for(int j = 0; j < pn && i * p[j] <= n; j++) {
flag[i * p [j]] = true;
if(i % p[j] == 0) {
mu[i * p[j]] = 0;
break;
} else mu[i * p[j]] = -mu[i];
}
}
}
LL inv[200005];
LL fact[200005];
LL ifac[200005];
LL comb(LL a,LL b){
return fact[a]*ifac[b]%MOD*ifac[a-b]%MOD;
}
LL play(int n,int m){
return comb(n+m-1,n-1);
}
int N,M,K,n;
LL solve(int n,int M){
LL ans=0;
for(int i=0;i<=n&&i*K<=M;i++){
LL mul=comb(n,i);
LL add=play(n,M-i*K);
if(i&1)ans-=mul*add%MOD;
else ans+=mul*add%MOD;
}
return ans%MOD;
}
LL g(int x){
int d=n/x;
if(M%d)return 0;
return solve(x,M/d);
}
LL gao(int x){
int y=x;
vector<int>L;
for(int i=2;i*i<=x;i++)if(x%i==0){
L.PB(i);
while(x%i==0)x/=i;
}
if(x>1)L.PB(x);
x=y;
LL ret=0;
for(int i=0;i<1<<L.SZ;i++){
int d=1,mu=1;
for(int j=0;j<L.SZ;j++)if(i>>j&1)
d*=L[j],mu=-mu;
ret+=mu*inv[d];
}
return ret%MOD;
}
int main(){
init();
int i,j,_T;
for(inv[0]=inv[1]=1,i=2;i<=200001;i++)
inv[i]=inv[MOD%i]*(MOD-MOD/i)%MOD;
for(fact[0]=i=1;i<=200001;i++)
fact[i]=fact[i-1]*i%MOD;
for(ifac[0]=i=1;i<=200001;i++)
ifac[i]=ifac[i-1]*inv[i]%MOD;
scanf("%d",&_T);
for(int CA=1;CA<=_T;CA++){
scanf("%d%d%d",&N,&M,&K);
printf("Case #%d: ",CA);
n=N-M;
if(n==0)printf("%d\n",N>=K?0:1);
else {
int gg=__gcd(n,M);
set<int>SD;
for(i=1;i*i<=gg;i++)if(gg%i==0)
SD.insert(i),SD.insert(gg/i);
vector<int>D(SD.OP,SD.ED);
LL ans=0;
map<int,LL>W;
for(i=0;i<D.SZ;i++){
int u=D[i],v=n/u;
for(int w=1;w*w<=v;w++)if(v%w==0){
int d=w;
W[d]+=inv[v]*mu[v/d];
if(w*w!=v){
d=v/w;
W[d]+=inv[v]*mu[v/d];
}
}
}
for(map<int,LL>::iterator it=W.OP;it!=W.ED;++it)
ans+=(*it).BB%MOD*g((*it).AA);
ans=(ans%MOD+MOD)%MOD;
printf("%d\n",int(ans));
}
}
return 0;
}