Counting Bishops

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