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] $ .