codeforces Gym

拓展Lucas

#include<cstdio>
#include<cstdlib>
#include<algorithm>
#include<cstring>
#include<vector>
#define MAXN 100000+10
#define ll long long
#define pb push_back
#define ft first
#define sc second
#define mp make_pair
using namespace std;
void extgcd(ll a,ll b,ll &x,ll &y){
    if(!b){x=1,y=0;}
    else{
        ll xx,yy;
        extgcd(b,a%b,xx,yy);
        x=yy;
        y=xx-a/b*yy;
    }
}
ll Inv(ll a,ll b){
    ll x,y;
    extgcd(a,b,x,y);
    x=(x%b+b)%b;
    if(!x)x+=b;
    return x;
}
ll Pow(ll a,ll b,ll p){
    ll ret=1LL;
    while(b){    
        if(b&1){(ret*=a)%=p;}
        (a*=a)%=p;
        b>>=1;
    }
    return ret;
}
ll fac(ll n,ll pi,ll pk){
    if(!n)return 1LL;
    ll ret=1LL;
    for(ll i=2;i<pk;i++){
        if(i%pi)(ret*=i)%=pk;    
    }
    ret=Pow(ret,n/pk,pk);
    for(ll i=2;i<=(n%pk);i++){
        if(i%pi)(ret*=i)%=pk;    
    }
    return ret*fac(n/pi,pi,pk)%pk;
    //每隔pi拿走一个,所以是n/pi,不是n/pk 
}
ll C(ll n,ll m,ll pi,ll pk){
    ll a=fac(n,pi,pk),b=fac(m,pi,pk),c=fac(n-m,pi,pk);
    ll t=0LL;
    for(ll i=n/pi;i;i/=pi)t+=i;
    for(ll i=m/pi;i;i/=pi)t-=i;
    for(ll i=(n-m)/pi;i;i/=pi)t-=i;
    ll ret=a*Inv(b,pk)*Inv(c,pk)%pk;
    (ret*=Pow(pi,t,pk))%=pk;
    return ret;
}
ll n,m,p;
int main()
{
    ll ans=0LL;
    scanf("%lld%lld%lld",&n,&m,&p);
    for(ll x=p,i=2;i<=p;i++){
        if(x%i==0){
            ll pk=1;
            while(x%i==0){
                pk*=i;
                x/=i;
            }
            ll t=C(n,m,i,pk);
            (t*=(p/pk))%=p;
            (t*=Inv(p/pk,pk))%=p;
            (ans+=t)%=p;
        }
    }
    printf("%lld
",ans);
    return 0;
}