JZPKIL
终于A掉JZPKIL了。。 感觉以后可以当数论题模板了(Bernoulli数、Pollard's rho、Miller Rabin、*快速乘、快速幂、逆元、组合数)
推导见 ydc blog
最神奇的是gyz的O(1)快速乘
证明见:http://tieba.baidu.com/p/2175344676
刷到R1了 好开心
#include
#include
#include
#include
#include
#include
#define mod 1000000007
#define abs(x) ((x)>0?(x):(-(x)))
using namespace std;
typedef long long LL;
LL p[20000],prime[20000];
int num[20000],tot;
LL P[20000],Q[20000],B[20000];
LL b[3010];
int t[3010][3010],c[3010][3010];
int cnt;
LL mul(LL x,LL y,LL z){return (x*y-(LL)(x/(long double)z*y+1e-3)*z+z)%z;}
inline LL power(LL p,LL n,LL mo)
{
LL ans=1;
for(;n;n>>=1,p=mul(p,p,mo))
if(n&1)
ans=mul(ans,p,mo);
return ans;
}
LL power1(LL a,LL b,LL mo)
{
if (b==0) return 1;
if (b==1) return a%mo;
LL m=power1(a,b/2,mo);
m=(m*m)%mo;
if (b&1) m=(m*a)%mo;
return m;
}
inline bool Miller_Rabin(int p,LL n)
{
int s=0;
LL d=n-1;
while(!(d&1))
++s,d>>=1;
LL w=power(p,d,n);
if(w==1)
return true;
for(int i=0;i<=s-1;++i)
{
if(w==n-1)
return true;
w=mul(w,w,n);
}
return false;
}
inline bool isPrime(LL n)
{
static int nd[]={2,3,5,7,11,13,17,19,23};
if(n==1)
return false;
if(find(nd,nd+9,n)!=nd+9)
return true;
if(!(n&1))
return false;
for(int i=0;i<9;++i)
if(!Miller_Rabin(nd[i],n))
return false;
return true;
}
LL gcd(LL a,LL b)
{
if (b==0) return a;
else return gcd(b,a%b);
}
void frac(LL n)
{
if(isPrime(n))
{
p[++cnt]=n;
return ;
}
int c=16831;
while(1)
{
LL x1,x2;
int i=1,k=2;
x1=x2=1;
while(1)
{
x1=mul(x1,x1,n)+c;
x1%=n;
LL d=gcd(abs(x1-x2),n);
if(d!=1&&d!=n)
{
frac(d),frac(n/d);
return ;
}
if(x1==x2)
break;
if(++i==k)
k<<=1,x2=x1;
}
c--;
}
}
LL exgcd(LL a,LL b,LL &x,LL &y)
{
if (b==0)
{
x=1,y=0;
return a;
}
LL r=exgcd(b,a%b,x,y);
LL t=x;
x=y;
y=t-a/b*y;
return r;
}
LL anti(LL n)
{
LL x,y;
exgcd(n,mod,x,y);
x=x%mod;
if (x<0) x+=mod;
return x;
}
void init()
{
int n=3000;
c[0][0]=1;
for (int i=1;i<=n+1;++i)
{
c[i][0]=1;
for (int j=1;j<=i;++j)
{
c[i][j]=c[i-1][j]+c[i-1][j-1];
if (c[i][j]>=mod) c[i][j]-=mod;
}
}
for (int i=0;i<=n;++i)
{
b[i]=i+1;
for (int j=0;j=1) a-=(kil[i]*super[i][num[i]-j-1])%mod;
a%=mod;
if (a<0) a+=mod;
tmp+=kk*a;
kk*=jzp[i];
kk%=mod;
tmp%=mod;
d*=prime[i];
}
res=res*tmp;
res%=mod;
}
return res;
}
LL work(LL n,int x,int y)
{
cnt=0,tot=0;
frac(n);
sort(p+1,p+cnt+1);
add(n,p[1]);
for (int i=2;i<=cnt;++i)
if (p[i]!=p[i-1]) add(n,p[i]);
LL ans=0;
for (int i=1;i<=tot;++i)
{
kil[i]=power1(prime[i]%mod,y,mod);
jzp[i]=power1(prime[i]%mod,x,mod);
m[i]=power1(prime[i],num[i],n+1);
LL d=1;
for (int j=0;j<=num[i];++j,d*=prime[i]) super[i][j]=d%mod;
}
for (int i=y;i>=0;--i)
{
ans+=(t[y][i]*calc(n,i,x,y))%mod;
ans%=mod;
if (ans<0) ans+=mod;
for (int i=1;i<=tot;++i)
{
LL d=1;
for (int j=0;j<=num[i];++j,d*=prime[i]) super[i][j]=(super[i][j]*(d%mod))%mod;
}
}
n%=mod;
ans=(ans*power1(n,y,mod))%mod;
return ans;
}
LL kill(LL n,int x,int y)
{
LL ans=0,p=n%mod,d=p;
for(int i=y;i>=0;--i)
{
ans=ans+t[y][i]*d;
if(ans>=mod)
ans%=mod;
d=d*p;
if(d>=mod)
d%=mod;
}
return ans*power1(p,y,mod)%mod;
}
int main()
{
int T;LL n;
int x,y;
init();
cin>>T;
while (T--)
{
cin>>n>>x>>y;
//frac(n);
if (x==y) cout<