No Prime Differences

Description:

Input:

The first line of the input contains a single integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases. The description of the test cases follows.

The first and only line of each test case contains two integers $$$n$$$ and $$$m$$$ ($$$4 \le n, m \le 1000$$$) — the dimensions of the grid.

It is guaranteed that the sum of $$$n\cdot m$$$ over all test cases does not exceed $$$10^6$$$.

Output:

For each test case, output $$$n$$$ lines of $$$m$$$ integers each, representing the final grid. Every number from $$$1$$$ to $$$n\cdot m$$$ should appear exactly once in the grid.

The extra spaces and blank lines in the sample output below are only present to make the output easier to read, and are not required.

If there are multiple solutions, print any of them.

Sample Input:

3
4 4
5 7
6 4

Sample Output:

16  7  1  9
12  8  2  3
13  4 10 11
14  5  6 15

29 23 17  9  5  6  2
33 27 21 15 11  7  1
32 31 25 19 20 16 10
26 30 24 18 14  8  4
35 34 28 22 13 12  3

 2  3  7 11
 8  9  1 10
17 13  5  4
18 14  6 12
19 23 15 21
20 24 16 22

Note:

The first sample case corresponds to the picture above. The only absolute differences between adjacent elements in this grid are $$$1$$$, $$$4$$$, $$$6$$$, $$$8$$$, and $$$9$$$, none of which are prime.