51nod 1120 机器人走方格V3 卡特兰数+卢卡斯定理

#include <iostream>
#include <string.h>
#include <stdio.h>
#include <math.h>
using namespace std;
typedef long long ll;
const int maxn= 10010;
const int mod=10007;
int  f[10020];
void init()
{
f[0]=1;
for(int i=1;i<=maxn;i++)
f[i]=(i*f[i-1])%mod;

}

long long pow1(long long  n,long long m )
{
long long ans = 1;
while(m > 0)
{
if(m & 1)ans = (ans * n) % mod;
m = m >> 1;
n = (n * n) % mod;}
return ans;
}
long long lucas(ll n,ll m)
{
ll ans=1;
while(n&&m)
{
ll x,y;
x=n%mod;y=m%mod;
if(x<y)
return 0;
//printf("%lld %lld %d %d %d\n",x,y,f[x],f[y],f[x-y]);
ans=ans*f[x]*pow1(f[y]*f[x-y]%mod,mod-2)%mod;
n/=mod;m/=mod;
}
return ans%mod;
}
int main()
{   init();
ll n,m,t;
//freopen("out.txt","w",stdout);
while(~scanf("%lld",&n))
{
ll t=pow1(n,mod-2);
printf("%lld\n",2*lucas(2*n-2,n-1)*t%mod);
}
return 0;
}