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>
int main() {
  int W, H, N;
  int x[100], y[100], a[100];
  int XU, XL = 0, YU, YL = 0, X, Y;
  scanf("%d %d %d", &W, &H, &N);
  XU = W;
  YU = H;
  for (int i = 0; i < N; i++) scanf("%d %d %d", &x[i], &y[i], &a[i]);
  for (int i = 0; i < N; i++) switch (a[i]) {
      case 1:
        XL = x[i];
        break;
      case 2:
        XU = x[i];
        break;
      case 3:
        YL = y[i];
        break;
      case 4:
        YU = y[i];
        break;
      default:
        break;
    }
  X = XU - XL;
  Y = YU - YL;
  if (X < 0) X = 0;
  if (Y < 0) Y = 0;
  printf("%d", X * Y);
  return 0;
}
