CF2008H Sakurako's Test

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 $ . $ ^{\text{∗}} $ The median of an array of length $ n $ is the element that stands in the middle of the sorted array (at the $ \frac{n+2}{2} $ -th position for even $ n $ , and at the $ \frac{n+1}{2} $ -th for odd)

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.

For each test case, output $ q $ integers — the answer for each query.