lucas定理模板

适用于求组合数C(n,n+m), n,m<10^18,

#include <iostream>#include <cstdio>#include <algorithm>#include <cmath>#include <cstring>using namespace std;typedef long long lld;lld  n, m, p;lld Ext_gcd(lld a,lld b,lld &x,lld &y){   if(b==0) { x=1, y=0; return a; }   lld ret= Ext_gcd(b,a%b,y,x);   y-= a/b*x;   return ret;}lld Inv(lld a,int m){   ///求逆元   lld d,x,y,t= (lld)m;   d= Ext_gcd(a,t,x,y);   if(d==1) return (x%t+t)%t;   return -1;}lld Cm(lld n, lld m, lld p)  ///组合数学{    lld a=1, b=1;    if(m>n) return 0;    while(m)    {        a=(a*n)%p;        b=(b*m)%p;        m--;        n--;    }    return (lld)a*Inv(b,p)%p;  ///（a/b）%p 等价于 a*（b，p）的逆元}int Lucas(lld n, lld m, lld p)  ///把n分段递归求解相乘{    if(m==0) return 1;    return (lld)Cm(n%p,m%p,p)*(lld)Lucas(n/p,m/p,p)%p;}int main(){    while(scanf("%lld%lld%lld",&n,&m,&p))    {        if(n==0&&m==0&&p==0)            break;        printf("%d\n",Lucas(n+m,m,p));    }    return 0;}