CF2077F AND x OR

Suppose you have two arrays $ c $ and $ d $ , each of length $ k $ . The pair $ (c, d) $ is called good if $ c $ can be changed to $ d $ by performing the following operation any number of times. - Select two distinct indices $ i $ and $ j $ ( $ 1 \leq i, j \leq k $ , $ i \neq j $ ) and a nonnegative integer $ x $ ( $ 0 \leq x < 2^{30} $ ). Then, apply the following transformations: - $ c_i := c_i \mathbin{\&} x $ , where $ \& $ denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND). - $ c_j := c_j \mathbin{|} x $ , where $ | $ denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#OR). You are given two arrays $ a $ and $ b $ , both of length $ n $ , containing nonnegative integers not exceeding $ m $ . You can perform two types of moves on these arrays any number of times: 1. Select an index $ i $ ( $ 1 \leq i \leq n $ ) and set $ a_i := a_i + 1 $ . 2. Select an index $ i $ ( $ 1 \leq i \leq n $ ) and set $ b_i := b_i + 1 $ . Note that the elements of $ a $ and $ b $ may exceed $ m $ at some point while performing the moves. Find the minimum number of moves required to make the pair $ (a, b) $ good.

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^4 $ ). The description of the test cases follows. The first line of each test case contains two integers $ n $ and $ m $ ( $ 1 \leq n, m \leq 2 \cdot 10^6 $ ) — the length of arrays $ a $ and $ b $ , and the maximum possible value in these arrays, respectively. The second line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 0 \leq a_i \leq m $ ) — denoting the array $ a $ . The third line contains $ n $ integers $ b_1, b_2, \ldots, b_n $ ( $ 0 \leq b_i \leq m $ ) — denoting the array $ b $ . Additionally, it is guaranteed that the sum of all values of $ n $ and the sum of all values of $ m $ across all test cases do not exceed $ 2 \cdot 10^6 $ .

For each test case, output a single integer — the minimum number of moves required to make the pair $ (a, b) $ good.

In the first case, we already have $ a = b $ . In the second case, we can perform move $ 2 $ on index $ i = 2 $ twice. The array $ b $ becomes $ [8, 8, 32] $ . We can see that $ (a, b) $ is now good. In the third case, we can perform move $ 2 $ on index $ i = 1 $ , then perform move $ 1 $ on index $ i = 2 $ . It can be proven that you cannot make the pair $ (a, b) $ good in fewer than $ 2 $ moves.