B. Deja Vutime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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.OutputFor each test case, output the array after all of the modification queries.ExampleInput
45 31 2 3 4 42 3 47 37 8 12 36 48 6 310 4 25 42 2 2 2 21 1 1 15 51 2 4 8 165 2 3 4 1Output
1 2 3 6 6 
7 10 14 38 58 6 3 
3 3 3 3 3 
1 3 7 11 19 
NoteIn 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].
45 31 2 3 4 42 3 47 37 8 12 36 48 6 310 4 25 42 2 2 2 21 1 1 15 51 2 4 8 165 2 3 4 1
1 2 3 6 6  7 10 14 38 58 6 3  3 3 3 3 3  1 3 7 11 19  
['brute force', 'math', 'sortings', '*1100']