Li Hua and Pattern

Description:

Input:

The first line contains the single integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases.

The first line of each test case contains two integers $$$n,k$$$ ($$$1\le n\le 10^3,0\le k \le 10^9$$$) — the size of the pattern and the number of operations.

Each of next $$$n$$$ lines contains $$$n$$$ integers $$$a_{i,j}$$$ ($$$a_{i,j}\in\{0,1\}$$$) — the initial color of the cell, $$$0$$$ for blue and $$$1$$$ for red.

It's guaranteed that sum of $$$n$$$ over all test cases does not exceed $$$10^3$$$.

Output:

For each set of input, print "YES" if it's possible to make the pattern, that matches its rotation by $$$180^{\circ}$$$ after applying exactly $$$k$$$ of operations, and "NO" otherwise.

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

Sample Input:

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

Sample Output:

NO
YES
YES

Note:

In test case 1, you can't perform any operation. The pattern after rotation is on the right.

In test case 2, you can perform operations on $$$(2,1),(3,2),(3,4)$$$. The pattern after operations is in the middle and the pattern after rotation is on the right.