Alphabet Soup HDU - 4187

 1 #include <bits/stdc++.h>
 2 using namespace std;
 3 #define LL long long 
 4 const int mod = 1e8 + 7;
 5 const int maxn = 360010;
 6 int a[maxn], b[maxn];
 7 int f[maxn];
 8 void getf(int m){
 9     f[0] = f[1] = 0;
10     for(int i = 1; i < m; i++){
11         int j = f[i];
12         while(j && b[i] != b[j]) j = f[j];
13         f[i + 1] = b[i] == b[j] ? j + 1 : 0;
14     }
15 }
16 LL quickpow(LL a, LL b, LL mod){
17     LL temp = a % mod, res = 1;
18     while(b){
19         if(b & 1) res = res * temp % mod;
20         b >>= 1;
21         temp = temp * temp % mod;
22     }
23     return res;
24 }
25 int main(){
26     //freopen("in.txt", "r", stdin);
27     int n, m;
28     while(scanf("%d %d", &n, &m) && (n + m) > 0){
29         for(int i = 0; i < m; i++){
30             scanf("%d", &a[i]);
31         }
32         sort(a, a + m);
33         for(int i = 0; i < m; i++){
34             b[i] = a[(i + 1) % m] - a[i];
35             if(b[i] < 0) b[i] += 360000;
36         }
37         getf(m);
38         int cir = m - f[m];
39         //cout<<cir<<endl;
40 //        int cnt;
41 //        if(m % cir == 0) cnt = m / cir;
42 //        else cnt = m;
43         LL ans = 0;
44         int rt = 0;
45         for(int i = 0; i < m; i++){
46             if(i % cir == 0) {
47                 ans = ans + quickpow(n, __gcd(i, m), mod);
48                 rt++;
49                 if(ans >= mod) ans %= mod;
50             }
51         }
52         ans = ans * quickpow(rt, mod - 2, mod) % mod;
53         printf("%lld\n", ans);
54     }
55 }