372. Super Pow

I don’t have any clue. This is completely a math problem. I have to follow the top rated solution.

1:  class Solution {  
2:  private:  
3:    const int k = 1337;  
4:    int powmod(int a, int b) {  
5:      // (a^b)%k = (a^(b-1)*a)%k = (a^(b-1)%k)*(a%k)%k  
6:      int res = 1;  
7:      a %= k;  
8:      for (int i = 0; i < b; i++) {  
9:        res = res * a % k;  
10:      }  
11:      return res;  
12:    }  
13:  public:  
14:    int superPow(int a, vector<int>& b) {  
15:      // ab % k = (a%k)(b%k)%k  
16:      // a^123 % k = (a^120*a^3) % k = (a^120%k)(a^3%k)%k  
17:      if (b.empty()) return 1;  
18:      int last = b.back();  
19:      b.pop_back();  
20:      return powmod(superPow(a, b), 10) * powmod(a, last) % k;  
21:    }  
22:  };