D. Zero is not an option!
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You will be given $$$T$$$ test cases.

In each test case, you are given a grid of size $$$N \times M$$$ containing integers. Your task is to choose exactly one number from each row so that the bitwise AND of all the chosen numbers is strictly greater than $$$0$$$.

Formally, you need to choose integers $$$c_1, c_2, \dots, c_{N}$$$ with $$$1 \le c_i \le M$$$ such that $$$$$$ a_{1,c_1} \;\&\; a_{2,c_2} \;\&\; \cdots \;\&\; a_{N,c_N} \; \gt \; 0, $$$$$$ where $$$a_{i,j}$$$ denotes the element in the $$$i$$$-th row and $$$j$$$-th column of the grid.

Input

The first line contains a single integer $$$T$$$ ($$$1 \le T \le 2 \cdot 10^5$$$) — the number of test cases.

The first line of each test case contains two integers $$$N$$$ and $$$M$$$ — the number of rows and columns in the grid. Then follow $$$N$$$ lines, each containing $$$M$$$ integers — the elements of the grid $$$a_{i,j}$$$.

Constraints

$$$1 \le N, M \le 2 \cdot 10^5$$$

$$$0 \le a_{i,j} \le 10^{14}$$$

$$$1 \le \sum (N \cdot M) \le 2 \cdot 10^5$$$ over all test cases.

Output

For each test case, print YES if it is possible to choose exactly one number from each row such that their bitwise AND is greater than $$$0$$$. Otherwise, print NO.

Examples
Input
1
2 2
3 3
4 8
Output
NO
Input
1
2 3
3 5 8
4 1 16
Output
YES
Note

Test 1. The grid is: 


3 3
4 8
We must choose one number from each row. Some possible pairs are: $$$(3,4) \Rightarrow 3 \& 4 = 0$$$ , $$$(3,8) \Rightarrow 3 \& 8 = 0$$$ . No matter how we choose, the bitwise AND is $$$0$$$. Hence the answer is NO.

Test 2. The grid is: 


3 5 8
4 1 16
If we pick $$$5$$$ from the first row and $$$1$$$ from the second row, then $$$5 \& 1 = 1 \gt 0$$$. So a valid selection exists. Hence the answer is YES.