Neighbor Grid

Description:

Input:

The input consists of multiple test cases. The first line contains an integer $$$t$$$ ($$$1 \le t \le 5000$$$)  — the number of test cases. The description of the test cases follows.

The first line of each test case contains two integers $$$n$$$ and $$$m$$$ ($$$2 \le n, m \le 300$$$)  — the number of rows and columns, respectively.

The following $$$n$$$ lines contain $$$m$$$ integers each, the $$$j$$$-th element in the $$$i$$$-th line $$$a_{i, j}$$$ is the number written in the $$$j$$$-th cell of the $$$i$$$-th row ($$$0 \le a_{i, j} \le 10^9$$$).

It is guaranteed that the sum of $$$n \cdot m$$$ over all test cases does not exceed $$$10^5$$$.

Output:

If it is impossible to obtain a good grid, print a single line containing "NO".

Otherwise, print a single line containing "YES", followed by $$$n$$$ lines each containing $$$m$$$ integers, which describe the final state of the grid. This final grid should be obtainable from the initial one by applying some operations (possibly zero).

If there are multiple possible answers, you may print any of them.

Sample Input:

5
3 4
0 0 0 0
0 1 0 0
0 0 0 0
2 2
3 0
0 0
2 2
0 0
0 0
2 3
0 0 0
0 4 0
4 4
0 0 0 0
0 2 0 1
0 0 0 0
0 0 0 0

Sample Output:

YES
0 0 0 0
0 1 1 0
0 0 0 0
NO
YES
0 0
0 0
NO
YES
0 1 0 0
1 4 2 1
0 2 0 0
1 3 1 0

Note:

In the first test case, we can obtain the resulting grid by increasing the number in row $$$2$$$, column $$$3$$$ once. Both of the cells that contain $$$1$$$ have exactly one neighbor that is greater than zero, so the grid is good. Many other solutions exist, such as the grid

$$$$$$0\;1\;0\;0$$$$$$ $$$$$$0\;2\;1\;0$$$$$$ $$$$$$0\;0\;0\;0$$$$$$

All of them are accepted as valid answers.

In the second test case, it is impossible to make the grid good.

In the third test case, notice that no cell has a number greater than zero on it, so the grid is automatically good.