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 by
grid of distinct integers from
to
such that it has exactly
peaks.
Constraints
Subtask 1 [30%]
Subtask 2 [70%]
No additional constraints.
Input Specification
The first and only line contains the space-separated integers and
.
Output Specification
Output lines containing
space-separated integers, a grid of size
by
which contains each integer from
to
such that there are exactly
peaks. If there are multiple solutions, output any of them. If such a grid does not exist, output
.
Sample Input
3 2
Sample Output
9 1 2
8 7 5
4 3 6
Explanation for Sample
and
are the
peaks.
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