E. Another Filling the Grid
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You have $$$n \times n$$$ square grid and an integer $$$k$$$. Put an integer in each cell while satisfying the conditions below.

  • All numbers in the grid should be between $$$1$$$ and $$$k$$$ inclusive.
  • Minimum number of the $$$i$$$-th row is $$$1$$$ ($$$1 \le i \le n$$$).
  • Minimum number of the $$$j$$$-th column is $$$1$$$ ($$$1 \le j \le n$$$).

Find the number of ways to put integers in the grid. Since the answer can be very large, find the answer modulo $$$(10^{9} + 7)$$$.

These are the examples of valid and invalid grid when $$$n=k=2$$$.
Input

The only line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 250$$$, $$$1 \le k \le 10^{9}$$$).

Output

Print the answer modulo $$$(10^{9} + 7)$$$.

Examples
Input
2 2
Output
7
Input
123 456789
Output
689974806
Note

In the first example, following $$$7$$$ cases are possible.

In the second example, make sure you print the answer modulo $$$(10^{9} + 7)$$$.