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| #include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
#include <queue>
using namespace std;
typedef long long LL;
const int maxn = 12;
const int maxm = 10010;
char s[maxn];
int a[maxn];
int phi[maxm];
void phi_table() {
phi[1] = 1;
for (int i = 2; i < maxm; ++i) {
if (!phi[i]) {
for (int j = i; j < maxm; j += i) {
if (!phi[j]) {
phi[j] = j;
}
phi[j] = phi[j] / i * (i - 1);
}
}
}
}
int pow_mod(int x, int k, int mod) {
if (x == 1 || k == 0) {
return 1;
}
int res = 1;
for (int i = 0; i < k; ++i) {
res *= x;
if (res >= mod) {
break;
}
}
if (res < mod) {
return res;
}
res = 1;
int cur = x;
while (k) {
if (k & 1) {
res = res * cur % mod;
}
cur = cur * cur % mod;
k >>= 1;
}
return res + mod;
}
int dfs(int d, int mod, int n) {
if (d == n) {
return a[d] >= mod ? a[d] % mod + mod : a[d];
}
return pow_mod(a[d], dfs(d + 1, phi[mod], n), mod);
}
int main() {
phi_table();
int t = 0;
while (~scanf("%s", s) && s[0] != '#') {
int n, m;
sscanf(s, "%d", &m);
scanf("%d", &n);
for (int i = 1; i <= n; ++i) {
scanf("%d", &a[i]);
}
printf("Case #%d: %d\n", ++t, dfs(1, m, n) % m);
}
return 0;
}
|