HDU5446 Unknown Treasure[中国剩余定理+Lucas]

Unknown Treasure

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<string>
#include<algorithm>
#include<queue>
#include<stack>
#include<set>
#include<map>
#include<vector>
using namespace std;
typedef long long ll;
const int N=15;
const int maxn=1e5+5;
ll n,m;
int k;
int prim
;
ll a
;
ll fac[maxn];
void initial(int mod)
{
fac[0]=1;
for (int i=1 ; i<mod+1 ; ++i)
fac[i]=fac[i-1]*i%mod;
}
ll Pow(ll n,ll m,ll mod)
{
n%=mod;
ll res=1;
while (m)
{
if (m&1)
res=res*n%mod;
n=n*n%mod;
m>>=1;
}
return res;
}
ll C(ll n,ll m,ll p)
{
if (n<m)
return 0;
return fac
*Pow(fac[m]*fac[n-m],p-2,p)%p;
}
ll lucas(ll n,ll m,ll p)
{
if (!n || !m)
return 1;
return lucas(n/p,m/p,p)*C(n%p,m%p,p)%p;
}
ll exgcd(ll a,ll b,ll &x,ll &y)
{
if (!b)
{
x=1;
y=0;
return a;
}
ll gcd=exgcd(b,a%b,x,y);
ll tmp=x;
x=y;
y=tmp-a/b*x;
return gcd;
}
ll add(ll a,ll b,ll m)
{
ll ans=0;
while (b)
{
if (b&1)
ans=(ans+a)%m;
a=(a+a)%m;
b>>=1;
}
return ans;
}
ll crt(ll a[],int m[],int n)
{
ll M=1;
ll ans=0;
for (int i=0 ; i<n ; ++i)
M*=m[i];
for (int i=0 ; i<n ; ++i)
{
ll x,y;
ll Mi=M/m[i];
exgcd(Mi,m[i],x,y);
ans=(ans+add(add(x,Mi,M),a[i],M)+M)%M;
}
if (ans<0)
ans+=M;
return ans;
}
int main()
{
int T;
scanf("%d",&T);
while (T--)
{
scanf("%lld%lld%d",&n,&m,&k);
for (int i=0 ; i<k ; ++i)
{
scanf("%d",&prim[i]);
initial(prim[i]);
a[i]=lucas(n,m,prim[i]);
}
printf("%lld\n",crt(a,prim,k));
}
return 0;
}