#include <stdio.h> #include <string.h> #include <math.h> #define LL long long LL a[20]; LL euler(LL n) { LL m=(LL)sqrt(n+0.5); LL ans=n; for(LL i=2;i<=m;i++) if(n%i==0){ ans=ans/i*(i-1); while(n%i==0)n/=i; } if(n>1)ans=ans/n*(n-1); return ans; } LL pmod(LL a,LL n,LL m) { LL now = 1; for(LL i=0;i<n;i++) { now *= a; if(now>=m) break; } if(now >= m) now = m; else now=0; if(n==0)return 1; LL x=pmod(a,n/2,m); LL ans=(LL)x*x%m; if(n%2==1) ans=ans*a%m; return ans+now; } LL solve(LL cur,LL n,LL m) { if(cur==n-1) { if(a[cur]>=m) return a[cur]%m+m; else return a[cur]; } LL M=euler(m); LL p=solve(cur+1,n,M); LL ans=pmod(a[cur],p,m); return ans; } int main() { char s[10]; LL m,n; int cas=0; while(scanf("%s",s)==1) { int l=strlen(s); if(s[0]=='#'&&l==1)break; m=0; for(int i=0;i<l;i++) m=m*10+s[i]-'0'; scanf("%lld",&n); for(int i=0;i<n;i++) scanf("%lld",&a[i]); printf("Case #%d: %lld\n",++cas,solve(0,n,m)%m); } return 0; } #include <stdio.h>#include <string.h>#include <math.h>#define LL long longLL a[20];LL euler(LL n){ LL m=(LL)sqrt(n+0.5); LL ans=n; for(LL i=2;i<=m;i++) if(n%i==0){ ans=ans/i*(i-1); while(n%i==0)n/=i; } if(n>1)ans=ans/n*(n-1); return ans;}LL pmod(LL a,LL n,LL m){ LL now = 1; for(LL i=0;i<n;i++) { now *= a; if(now>=m) break; } if(now >= m) now = m; else now=0; if(n==0)return 1; LL x=pmod(a,n/2,m); LL ans=(LL)x*x%m; if(n%2==1) ans=ans*a%m; return ans+now;}LL solve(LL cur,LL n,LL m){ if(cur==n-1) { if(a[cur]>=m) return a[cur]%m+m; else return a[cur]; } LL M=euler(m); LL p=solve(cur+1,n,M); LL ans=pmod(a[cur],p,m); return ans;}int main(){ char s[10]; LL m,n; int cas=0; while(scanf("%s",s)==1) { int l=strlen(s); if(s[0]=='#'&&l==1)break; m=0; for(int i=0;i<l;i++) m=m*10+s[i]-'0'; scanf("%lld",&n); for(int i=0;i<n;i++) scanf("%lld",&a[i]); printf("Case #%d: %lld\n",++cas,solve(0,n,m)%m); } return 0;}