Background

This problem was planned to redesign part of the scoring in early July.

Due to personal reasons, it is planned to be postponed.

Problem Description

This problem has $T$ test cases.

You need to construct $n$ permutations of length $m$ such that, for each of the $m$ numbers, the sum of the indices (indices start from $1$) of this number across the $n$ permutations are all equal. If there is no solution, output $-1$.

Input Format

The first line contains a positive integer $T$.

For each test case:

Input one line with two positive integers $n, m$.

Output Format

For each test case:

Output $n$ lines, each containing $m$ positive integers, or output a single line with an integer $-1$ to indicate your answer.

3
3 3
2 5
1 3

1 2 3
2 3 1
3 1 2
5 1 4 2 3
3 2 4 1 5
-1

Hint

For $100\%$ of the testdata, it is guaranteed that $1 \le T \le 10^6$, $1 \le n, m \le 10^6$, $\sum nm \le 10^6$.

Translated by ChatGPT 5