Sakurako will soon take a test. The test can be described as an array of integers $$$n$$$ and a task on it:

Given an integer $$$x$$$, Sakurako can perform the following operation any number of times:

- Choose an integer $$$i$$$ ($$$1\le i\le n$$$) such that $$$a_i\ge x$$$;
- Change the value of $$$a_i$$$ to $$$a_i-x$$$.

Using this operation any number of times, she must find the minimum possible median$$$^{\text{∗}}$$$ of the array $$$a$$$.

Sakurako knows the array but does not know the integer $$$x$$$. Someone let it slip that one of the $$$q$$$ values of $$$x$$$ will be in the next test, so Sakurako is asking you what the answer is for each such $$$x$$$.

Input format:
The first line contains one integer $$$t$$$ ($$$1\le t\le 10^4$$$)  — the number of test cases.

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

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1\le a_i\le n$$$)  — the elements of the array.

The following $$$q$$$ lines each contain one integer $$$x$$$ ($$$1\le x\le n$$$).

It is guaranteed that the sum of $$$n$$$ across all test cases does not exceed $$$10^5$$$. The same guarantee applies to the sum of $$$q$$$ across all test cases.
Output format:
For each test case, output $$$q$$$ integers  — the answer for each query.
Example Input 0:
2
5 5
1 2 3 4 5
1
2
3
4
5
6 3
1 2 6 4 1 3
2
1
5

Example Output 0:
0 1 1 1 2 
1 0 2



Example input:
2
5 5
1 2 3 4 5
1
2
3
4
5
6 3
1 2 6 4 1 3
2
1
5


Example output:
0 1 1 1 2 
1 0 2