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.