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Another Filling the Grid

1000ms 262144K

Description:

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

Sample Input:

2 2

Sample Output:

7

Sample Input:

123 456789

Sample Output:

689974806

Note:

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

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

Informação

Codeforces

Provedor Codeforces

Código CF1228E

Tags

combinatoricsdpmath

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Datas 09/05/2023 09:52:38

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