CF1891B.Deja Vu

You are given an array $a$ of length $n$ , consisting of positive integers, and an array $x$ of length $q$ , also consisting of positive integers.

There are $q$ modification. On the $i$ -th modification ( $1 \leq i \leq q$ ), for each $j$ ( $1 \leq j \leq n$ ), such that $a_j$ is divisible by $2^{x_i}$ , you add $2^{x_i-1}$ to $a_j$ . Note that $x_i$ ( $1 \leq x_i \leq 30$ ) is a positive integer not exceeding 30.

After all modification queries, you need to output the final array.

The first line contains a single integer $t$ ( $1 \leq t \leq 10^4$ ) — the number of test cases. The description of the test cases follows.

The first line of each test case contains two integers $n$ and $q$ ( $1 \leq n, q \leq 10^5$ ) —the length of the array $a$ and the number of queries respectively.

The second line of each test case contains $n$ integers $a_1, a_2, a_3, \ldots, a_n$ — the elements of the array $a$ ( $1 \leq a_i \leq 10^9$ ).

The third line of each test case contains $q$ integers $x_1, x_2, x_3, \ldots, x_q$ — the elements of the array $x$ ( $1 \leq x_i \leq 30$ ), which are the modification queries.

It is guaranteed that the sum of $n$ and the sum of $q$ across all test cases does not exceed $2 \cdot 10^5$ .

For each test case, output the array after all of the modification queries.

In the first test case, the first query will add $2$ to the integers in positions $4$ and $5$ . After this addition, the array would be $[1, 2, 3, 6, 6]$ . Other operations will not modify the array.

In the second test case, the first modification query does not change the array. The second modification query will add $8$ to the integer in position $5$ , so that the array would look like this: $[7, 8, 12, 36, 56, 6, 3]$ . The third modification query will add $2$ to the integers in positions $2, 3$ , $4$ and $5$ . The array would then look like this: $[7, 10, 14, 38, 58, 6, 3]$ .