Alice has an $n \times m$ matrix $a_{i,j}$ ($1 \le i \le n$, $1 \le j \le m$), where each element is a non-negative integer not exceeding $10^6$. Bob generated an $(n-1) \times (m-1)$ matrix $b_{i,j}$ ($1 \le i \le n-1$, $1 \le j \le m-1$) from this matrix, where each element is generated by the formula:

$$b_{i,j} = a_{i,j} + a_{i,j+1} + a_{i+1,j} + a_{i+1,j+1}$$

Now Alice has forgotten the matrix $a_{i,j}$. Please reconstruct $a_{i,j}$ based on the matrix $b_{i,j}$ provided by Bob.

Input

The input contains multiple test cases. The first line contains an integer $T$ representing the number of test cases. For each test case, the first line contains two positive integers $n, m$, representing the size of the matrix $a_{i,j}$. The next $n-1$ lines each contain $m-1$ non-negative integers, representing $b_{i,j}$.

Output

For each test case: 1. If the matrix $b_{i,j}$ cannot be generated, output a single line containing the string NO. 2. If the matrix $b_{i,j}$ can be generated, first output a single line containing the string YES, followed by $n$ lines, each containing $m$ non-negative integers (separated by single spaces) not exceeding $10^6$, representing $a_{i,j}$. If there are multiple matrices $a_{i,j}$ that can generate the given $b_{i,j}$, you may output any one of them.

Constraints

For all test cases: $1 \le T \le 10$, $2 \le n, m \le 300$, $0 \le b_{i,j} \le 4 \times 10^6$. The specific constraints for each test case are as follows:

Examples

Input 1

3
3 3
28 25
24 25
3 3
15 14
14 12
3 3
0 3000005
0 0

Output 1

YES
7 8 8
8 5 4
4 7 9
YES
4 2 2
5 4 6
5 0 2
NO