CodeVS1631 组合数

题

题解

代码

//卢卡斯定理
#include <cstdio>
#define ll long long
#define p 100003
using namespace std;
ll N, M, fac[p+100];
ll init()
{
ll i;
scanf("%lld%lld",&N,&M);
fac[0]=1;
for(i=1;i<p;i++)fac[i]=fac[i-1]*i%p;
}
void exgcd(ll a, ll b, ll &x, ll &y)
{
ll xx, yy;
if(!b){x=1,y=0;return;}
exgcd(b,a%b,xx,yy);
x=yy;y=xx-a/b*yy;
}
ll inv(ll a)
{
ll x, y;
exgcd(a,p,x,y);
return (x+p)%p;
}
ll C(ll n, ll m)
{return m>n?0:fac
*inv(fac[m]*fac[n-m]%p)%p;}
ll lacus(ll n, ll m)
{return m?C(n%p,m%p)*lacus(n/p,m/p):1;}
int main()
{
init();
printf("%lld\n",lacus(N,M));
return 0;
}