【数学/扩展欧几里得/Lucas定理】BZOJ 1951 :[Sdoi 2010]古代猪文

 1 #include<cstdio>
 2 #include<cstring>
 3 #include<cmath>
 4 #include<algorithm> 
 5 
 6 #define mo 999911659
 7 
 8 typedef long long ll;
 9 
10 using namespace std;
11 
12 int mod[5]={0,2,3,4679,35617};
13 
14 ll w[5],fac[5][36001];
15 
16 ll Qvod(ll x,ll k,ll mod)
17 {
18     ll ans=1;
19     while(k!=0)
20     {
21         if(k&1)ans=ans*x%mod;
22         x=x*x%mod;
23         k>>=1;
24     }
25     return ans;
26 }
27 
28 ll C(ll x,ll k,ll m)
29 {
30     if(x<k)return 0;
31     return fac[m][x]*Qvod(fac[m][k]*fac[m][x-k],mod[m]-2,mod[m])%mod[m];
32 }
33 
34 ll Lucas(ll x,ll k,int m)
35 {
36     if(x==0)return 1;
37     return Lucas(x/mod[m],k/mod[m],m)*C(k%mod[m],x%mod[m],m)%mod[m];
38 }
39 
40 ll x,y;
41 
42 void exgcd(ll n,ll m)
43 {
44     if(m==0){x=1,y=0;return;}
45     exgcd(m,n%m);
46     ll t=x;x=y,y=t-n/m*y;
47 }
48 
49 ll solve()
50 {
51     ll ans=0;
52     for(int i=1;i<=4;i++)
53     {
54         ll sb=(mo-1)/mod[i];
55         exgcd(sb,mod[i]);
56         ans=(ans+x*sb*w[i])%(mo-1);
57     }
58     if(ans<=mo-1)ans+=(mo-1);
59     return ans;
60 }
61 
62 int main()
63 {
64     for(int i=1;i<=4;i++)
65     {
66         fac[i][0]=1;
67         for(int j=1;j<=mod[i];j++)
68             fac[i][j]=fac[i][j-1]*j%mod[i];
69     }
70     int n,g;
71     scanf("%d%d",&n,&g);
72     if(g==mo){printf("0");return 0;}
73     g%=mo;
74     for(int i=1;i<=sqrt(n);i++)
75     {
76         if(n%i==0)
77         {
78             int tmp=n/i;
79             for(int j=1;j<=4;j++){
80                 if(tmp!=i)w[j]=(w[j]+Lucas(tmp,n,j));
81                 w[j]=(w[j]+Lucas(i,n,j))%mod[j];
82             }
83         }
84     }
85     printf("%lld",Qvod(g,solve(),mo));
86     return 0;
87 }