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.

见题面 Input 部分

见题面 Output 部分

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 $B$.