1 #include <iostream> 2 #include <string.h> 3 #include <string> 4 #include <fstream> 5 #include <algorithm> 6 #include <stdio.h> 7 #include <vector> 8 #include <queue> 9 #include <set> 10 #include <cmath> 11 using namespace std; 12 const double eps = 1e-8; 13 const double pi=acos(-1.0); 14 const int INF=0x7fffffff; 15 unsigned long long uINF = ~0LL; 16 #define MAXN 1007 17 typedef long long LL; 18 int phi[10010]; 19 void phi_table() 20 { 21 for(int i=2;i<=10000;i++) phi[i]=0; 22 phi[1]=1; 23 for(int i=2;i<=10000;i++) if(!phi[i]) 24 for(int j=i;j<=10000;j+=i) 25 { 26 if(!phi[j]) phi[j]=j; 27 phi[j]=phi[j]/i*(i-1); 28 } 29 } 30 int pow_mod(int a,int p,int n) 31 { 32 if(p==0)return 1; 33 int ans=pow_mod(a,p/2,n); 34 ans=ans*ans%n; 35 if(p%2==1)ans=ans*a%n; 36 return ans; 37 } 38 int n,m,a[11]; 39 bool Read() 40 { 41 string s; 42 cin>>s; 43 if(s=="#")return false; 44 m=0; 45 for(int i=0;i<s.length();i++) 46 { 47 m=m*10+(s[i]-'0'); 48 } 49 scanf("%d",&n); 50 for(int i=0;i<n;i++) 51 scanf("%d",&a[i]); 52 return true; 53 } 54 //a^x≡a^(x%phi(c)+phi(c))(mod c) 55 int dfs(int d,int mod) 56 { 57 if(d==n-1)return a[n-1]%mod; 58 int temp=dfs(d+1,phi[mod]); 59 int ans=pow_mod(a[d],temp+phi[mod],mod); 60 return ans; 61 } 62 int main() 63 { 64 int T=1; 65 //freopen("0.in","r",stdin); 66 phi_table(); 67 while(Read()) 68 { 69 printf("Case #%d: %d ",T++,dfs(0,m)); 70 } 71 72 return 0; 73 }
a^x≡a^(x%phi(c)+phi(c))(mod c)