B. Deja Vu
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Input

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 $$$2 \cdot 10^5$$$.

Output

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

Example
Input
4
5 3
1 2 3 4 4
2 3 4
7 3
7 8 12 36 48 6 3
10 4 2
5 4
2 2 2 2 2
1 1 1 1
5 5
1 2 4 8 16
5 2 3 4 1
Output
1 2 3 6 6 
7 10 14 38 58 6 3 
3 3 3 3 3 
1 3 7 11 19
Note

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: $$$[7, 10, 14, 38, 58, 6, 3]$$$.