Fishingprince is playing with an array $[a_1,a_2,\dots,a_n]$. He also has a magic number $m$.

He can do the following two operations on it:

• Select $1\le i\le n$ such that $a_i$ is divisible by $m$ (that is, there exists an integer $t$ such that $m \cdot t = a_i$). Replace $a_i$ with $m$ copies of $\frac{a_i}{m}$. The order of the other elements doesn't change. For example, when $m=2$ and $a=[2,3]$ and $i=1$, $a$ changes into $[1,1,3]$.
• Select $1\le i\le n-m+1$ such that $a_i=a_{i+1}=\dots=a_{i+m-1}$. Replace these $m$ elements with a single $m \cdot a_i$. The order of the other elements doesn't change. For example, when $m=2$ and $a=[3,2,2,3]$ and $i=2$, $a$ changes into $[3,4,3]$.

Note that the array length might change during the process. The value of $n$ above is defined as the current length of the array (might differ from the $n$ in the input).

Fishingprince has another array $[b_1,b_2,\dots,b_k]$. Please determine if he can turn $a$ into $b$ using any number (possibly zero) of operations.

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). Description of the test cases follows.

The first line of each test case contains two integers $n$ and $m$ ($1\le n\le 5\cdot 10^4$, $2\le m\le 10^9$).

The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1\le a_i\le 10^9$).

The third line of each test case contains one integer $k$ ($1\le k\le 5\cdot 10^4$).

The fourth line of each test case contains $k$ integers $b_1,b_2,\ldots,b_k$ ($1\le b_i\le 10^9$).

It is guaranteed that the sum of $n+k$ over all test cases does not exceed $2\cdot 10^5$.

Output

For each testcase, print Yes if it is possible to turn $a$ into $b$, and No otherwise. You can print each letter in any case (upper or lower).

见题面 Input 部分

见题面 Output 部分

In the first test case of the sample, we can do the second operation with $i=2$: $[1,\color{red}{2,2},4,2]\to [1,\color{red}{4},4,2]$.

In the second testcase of the sample, we can:

• do the second operation with $i=2$: $[1,\color{red}{2,2},8,2,2]\to [1,\color{red}{4},8,2,2]$.
• do the second operation with $i=4$: $[1,4,8,\color{red}{2,2}]\to [1,4,8,\color{red}{4}]$.
• do the first operation with $i=3$: $[1,4,\color{red}{8},4]\to [1,4,\color{red}{4,4},4]$.
• do the second operation with $i=2$: $[1,\color{red}{4,4},4,4]\to [1,\color{red}{8},4,4]$.
• do the second operation with $i=3$: $[1,8,\color{red}{4,4}]\to [1,8,\color{red}{8}]$.
• do the second operation with $i=2$: $[1,\color{red}{8,8}]\to [1,\color{red}{16}]$.