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