Your task is to count the number of ways k bishops can be placed on an n \times n chessboard so that no two bishops attack each other.

Two bishops attack each other if they are on the same diagonal.

Input

The only input line has two integers n and k: the board size and the number of bishops.

Output

Print one integer: the number of ways modulo 10^9+7.

Constraints

• 1 \le n \le 500
• 1 \le k \le n^2

Example

Input:

5 4

Output:

2728