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E. Another Filling the Grid

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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 $$$(10^{9} + 7)$$$.

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 $$$(10^{9} + 7)$$$.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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