Lucas(卢卡斯定理)模板

 

         Lucas用来求C(n,m)%p的值，适用于解决n,m较大，p(一定为素数)小于1e6的情况。

 

模板： 

#include 
#include 
#include 
#define ll long long
using namespace std;
const int maxn = 1e6+5;
const int mod = 1e9+7;
using namespace std;
ll quick_mod(ll a, ll b, ll c)
{
    ll ans = 1;
    while(b)
    {
        if(b & 1)
            ans = (ans*a)%c;
        b>>=1;
        a = (a*a)%c;
    }
    return ans;
}
ll fac[maxn];
void Get_Fac(ll m)///m!
{
    fac[0] = 1;
    for(int i=1; i<=m; i++)
        fac[i] = (fac[i-1]*i) % m;
}
ll Lucas(ll n, ll m, ll p)
{
    ll ans = 1;
    while(n && m)
    {
        ll a = n % p;
        ll b = m % p;
        if(a < b)
            return 0;
        ans = ( (ans*fac[a]%p) * (quick_mod(fac[b]*fac[a-b]%p,p-2,p)) ) % p;
        n /= p;
        m /= p;
    }
    return ans;
}
int main()
{
    ll n, m, p;
    cin>>n>>m>>p;
    Get_Fac(p);
    cout<