You are given two matrices $$$A$$$ and $$$B$$$ of size $$$n \times m$$$, filled with integers between $$$0$$$ and $$$10^9$$$. You can perform the following operations on matrix $$$A$$$ in any order and any number of times:

&=: choose two integers $$$i$$$ and $$$x$$$ ($$$1 \le i \le n$$$, $$$x \ge 0$$$) and replace each element in row $$$i$$$ with the result of the bitwise AND operation between $$$x$$$ and that element. Formally, for every $$$j \in [1, m]$$$, the element $$$A_{i,j}$$$ is replaced with $$$A_{i,j} \text{ & } x$$$;
|=: choose two integers $$$j$$$ and $$$x$$$ ($$$1 \le j \le m$$$, $$$x \ge 0$$$) and replace each element in column $$$j$$$ with the result of the bitwise OR operation between $$$x$$$ and that element. Formally, for every $$$i \in [1, n]$$$, the element $$$A_{i,j}$$$ is replaced with $$$A_{i,j} \text{ | } x$$$.

The value of $$$x$$$ may be chosen differently for different operations.

Determine whether it is possible to transform matrix $$$A$$$ into matrix $$$B$$$ using the given operations any number of times (including zero).

Input

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

Each test case is given as follows:

the first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n, m \le 10^3$$$; $$$n \cdot m \le 10^3$$$) — the dimensions of the matrices $$$A$$$ and $$$B$$$;
the following $$$n$$$ lines describe the matrix $$$A$$$, where the $$$i$$$-th line contains $$$m$$$ integers $$$A_{i,1}, A_{i,2}, \dots, A_{i,m}$$$ ($$$0 \le A_{i,j} \le 10^9$$$);
the following $$$n$$$ lines describe the matrix $$$B$$$, where the $$$i$$$-th line contains $$$m$$$ integers $$$B_{i,1}, B_{i,2}, \dots, B_{i,m}$$$ ($$$0 \le B_{i,j} \le 10^9$$$).

Output

For each test case, output Yes if it is possible to transform the matrix $$$A$$$ into the matrix $$$B$$$; otherwise, output No. Each letter can be output in any case, upper or lower.

Note

Let's consider the second set of input data and show a sequence of operations that transforms matrix $$$A$$$ into matrix $$$B$$$:

Initially, the matrix looks like this:

$$$\begin{bmatrix} 10&10\\ 42&42\\ \end{bmatrix}$$$

Apply an operation of the first type with parameters $$$i = 1$$$ and $$$x = 0$$$. As a result, we get the matrix:

$$$\begin{bmatrix} 0&0\\ 42&42\\ \end{bmatrix}$$$

Apply an operation of the first type with parameters $$$i = 2$$$ and $$$x = 0$$$. As a result, we get the matrix:

$$$\begin{bmatrix} 0&0\\ 0&0\\ \end{bmatrix}$$$

Apply an operation of the second type with parameters $$$j = 1$$$ and $$$x = 21$$$. As a result, we get the matrix:

$$$\begin{bmatrix} 21&0\\ 21&0\\ \end{bmatrix}$$$

Apply an operation of the second type with parameters $$$j = 2$$$ and $$$x = 21$$$. As a result, we get the matrix:

$$$\begin{bmatrix} 21&21\\ 21&21\\ \end{bmatrix}$$$

Thus, we have transformed matrix $$$A$$$ into matrix $$$B$$$.

Idx	Name	Rating
A	Coin Transformation	800
B	Digits	1100
C	Sums on Segments	1600
D	Problem about GCD	1800
E	Matrix Transformation	2300
F	Nim	2700
G	Problem with Queries	3000

Educational Codeforces Round 173 (Rated for Div. 2)