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;
int main() {
  int w, h, n;
  scanf("%d%d%d", &w, &h, &n);
  int l = 0, r = w, u = h, d = 0;
  for (int i = 1; i <= n; i++) {
    int x, y, a;
    scanf("%d%d%d", &x, &y, &a);
    if (a == 1 && x > l) l = x;
    if (a == 2 && x < r) r = x;
    if (a == 3 && y > d) d = y;
    if (a == 4 && y < u) u = y;
  }
  int ans = (r - l) * (u - d);
  if (ans >= 0)
    printf("%d\n", ans);
  else
    printf("0\n");
  return 0;
}
