CF1696C Fishingprince Plays With Array

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.

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 $ .

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).

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}] $ .