There are N balls placed in a row. AtCoDeer the deer is painting each of these in one of the K colors of his paint cans. For aesthetic reasons, any two adjacent balls must be painted in different colors.

Find the number of the possible ways to paint the balls.

Constraints

* 1≦N≦1000
* 2≦K≦1000
* The correct answer is at most 2^{31}-1.

Input

The input is given from Standard Input in the following format:


N K


Output

Print the number of the possible ways to paint the balls.

Examples

Input

2 2


Output

2


Input

1 10


Output

10
#include <bits/stdc++.h>
using namespace std;
long long int N, A, B, oA, oB, nA, nB;
long long int mx(long long int A, long long int B) { return A < B ? B : A; }
int main() {
  cin >> N;
  cin >> nA >> nB;
  oA = nA;
  oB = nB;
  for (int i = 1; i < N; i++) {
    cin >> A >> B;
    if (A == B) {
      nA = mx(nA, nB);
      nB = nA;
    } else {
      long long int rslt = mx((long long int)ceil(nA / (double)A),
                              (long long int)ceil(nB / (double)B));
      nA = rslt * A;
      nB = rslt * B;
    }
    oA = A;
    oB = B;
  }
  cout << (nA + nB) << endl;
}
