【HDOJ6608】Fansblog（威尔逊定理）

题意：给定质数p，求q!模p的值，其中q为小于p的最大质数

1e9<=p<=1e14

思路：根据质数密度近似分布可以暴力找q并检查

找到q后根据威尔逊定理：

 把q+1到p-1这一段的逆元移过去

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned int uint;
typedef unsigned long long ull;
typedef pair<int,int> PII;
typedef pair<ll,ll> Pll;
typedef vector<int> VI;
#define N  110000
#define M  1100000
#define fi first
#define se second
#define MP make_pair
#define pi acos(-1)
#define mem(a,b) memset(a,b,sizeof(a))
#define rep(i,a,b) for(int i=(int)a;i<=(int)b;i++)
#define per(i,a,b) for(int i=(int)a;i>=(int)b;i--)
#define lowbit(x) x&(-x)
#define Rand (rand()*(1<<16)+rand())
#define id(x) ((x)<=B?(x):m-n/(x)+1)
#define ls p<<1
#define rs p<<1|1

const ll MOD=998244353,inv2=(MOD+1)/2;
      double eps=1e-6;
      ll INF=1e14;


int read()
{
   int v=0,f=1;
   char c=getchar();
   while(c<48||57<c) {if(c=='-') f=-1; c=getchar();}
   while(48<=c&&c<=57) v=(v<<3)+v+v+c-48,c=getchar();
   return v*f;
}

int prime(ll x)
{
    ll t=sqrt(x);
    for(ll i=2;i<=t;i++)
     if(x%i==0) return 0;
    return 1;
}

ll mult(ll a,ll b,ll p)
{
    ll t=(a*b-ll((long double)a/p*b+1e-3)*p)%p;
    return t<0?t+p:t;
}

ll pw(ll x,ll y,ll p)
{
    ll t=1;
    while(y)
    {
        if(y&1) t=mult(t,x,p);
        x=mult(x,x,p);
        y>>=1;
    }
    return t;
}

int main()
{
    //freopen("1.in","r",stdin);
    //freopen("1.out","w",stdout);
    int cas=read();
    while(cas--)
    {
        ll n;
        scanf("%I64d",&n);
        ll k=n-2;
        if(n==3) k=2;
         else
         {
            while(k&&!prime(k)) k-=2;
         }
        ll ans=n-1;
        //printf("k=%I64d
",k);
        for(ll i=k+1;i<=n-1;i++)
        {
            //printf("i=%I64d
",i);
            ll t=pw(i,n-2,n);
            //printf("inv%I64d=%I64d
",i,t);
            ans=mult(ans,t,n);
        }


        printf("%I64d
",ans);
    }
    return 0;
}