Aschin is interested in the peaks of a grid. A peak is defined as an element of the grid that is the largest in both the row and column containing that element. Please impress Aschin by constructing an $N$ by $N$ grid of distinct integers from $1$ to $N^2$ such that it has exactly $K$ peaks.

Constraints

$1\le N\le 2\times {10}^3$

$1\le K\le N$

Subtask 1 [30%]

$1\le N\le 3$

Subtask 2 [70%]

No additional constraints.

Input Specification

The first and only line contains the space-separated integers $N$ and $K$.

Output Specification

Output $N$ lines containing $N$ space-separated integers, a grid of size $N$ by $N$ which contains each integer from $1$ to $N^2$ such that there are exactly $K$ peaks. If there are multiple solutions, output any of them. If such a grid does not exist, output $-1$.

Sample Input

3 2

Sample Output

9 1 2
8 7 5
4 3 6

Explanation for Sample

$6$ and $9$ are the $2$ peaks.