HDU-1852-Beijing 2008-一个神奇的公式求逆元

 1 #include<stdio.h>
 2 typedef long long ll;
 3 
 4 ll ksm(ll x,ll n,ll mod)
 5 {
 6     ll res=1;
 7     while(n>0)
 8     {
 9         if(n&1)
10             res=res*x%mod;
11         x=x*x%mod;
12         n>>=1;
13     }
14     return res%mod;
15 }
16 
17 
18 //S=2008^x,所有因子和   get the sum S of all positive integer divisors of 2008 N.
19 //M=S%k(已知k)  the rest of the division of S by K. The result is kept as M
20 //求2008^M%k
21 
22 int main()
23 {
24     ll n,k;
25     while(~scanf("%lld %lld",&n,&k))
26     {
27         if(n==0&&k==0)
28             break;
29         ll k2=ksm(2,3*n+1,k*250);
30         if(k2-1<0)
31             k2=k2-1+k;
32         else
33             k2--;
34 
35         ll k251=ksm(251,n+1,250*k);
36         if(k251-1<0)
37             k251=k251-1+k;
38         else
39             k251--;
40 
41         ll M=k2*(k251)%(250*k)/250;
42      //   ll M=k2*(k251/k)%(250*k);
43   //  ll M=k2*(k251/250)%(250*k); WA，注意一下
44         ll ans=ksm(2008,M,k);
45         printf("%lld\n",ans);
46     }
47     return 0;
48 }