CF 2015 ICL, Finals, Div. 1 J. Ceizenpok’s formula [Lucas定理]

http://codeforces.com/gym/100633/problem/J

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Lucas定理P不是质数裸题

#include <iostream>

#include <cstdio>

#include <cstring>

#include <algorithm>

#include <cmath>

using namespace std;

typedef long long ll;

inline ll read(){

    char c=getchar();ll x=,f=;

    while(c<''||c>''){if(c=='-')f=-;c=getchar();}

    while(c>=''&&c<=''){x=x*+c-'';c=getchar();}

    return x*f;

}

ll n,m,MOD;

ll Pow(ll a,ll b,ll P){

    ll ans=;

    for(;b;b>>=,a=a*a%P)

        if(b&) ans=ans*a%P;

    return ans;

}

void exgcd(ll a,ll b,ll &d,ll &x,ll &y){

    if(b==) d=a,x=,y=;

    else exgcd(b,a%b,d,y,x),y-=(a/b)*x;

}

ll Inv(ll a,ll n){

    ll d,x,y;

    exgcd(a,n,d,x,y);

    return d==?(x+n)%n:-;

}

ll Fac(ll n,ll p,ll pr){

    if(n==) return ;

    ll re=;

    for(ll i=;i<=pr;i++) if(i%p) re=re*i%pr;

    re=Pow(re,n/pr,pr);

    ll r=n%pr;

    for(int i=;i<=r;i++) if(i%p) re=re*i%pr;

    return re*Fac(n/p,p,pr)%pr;

}

ll C(ll n,ll m,ll p,ll pr){

    if(n<m) return ;

    ll x=Fac(n,p,pr),y=Fac(m,p,pr),z=Fac(n-m,p,pr);

    ll c=;

    for(ll i=n;i;i/=p) c+=i/p;

    for(ll i=m;i;i/=p) c-=i/p;

    for(ll i=n-m;i;i/=p) c-=i/p;

    ll a=x*Inv(y,pr)%pr*Inv(z,pr)%pr*Pow(p,c,pr)%pr;

    return a*(MOD/pr)%MOD*Inv(MOD/pr,pr)%MOD;

}

ll Lucas(ll n,ll m){

    ll x=MOD,re=;

    for(ll i=;i<=MOD;i++) if(x%i==){

        ll pr=;

        while(x%i==) x/=i,pr*=i;

        re=(re+C(n,m,i,pr))%MOD;

    }

    return re;

}

int main(){

    //freopen("in","r",stdin);

    n=read();m=read();MOD=read();

    printf("%I64d",Lucas(n,m));

}