CF1833B Restore the Weather

You are given an array $ a $ containing the weather forecast for Berlandia for the last $ n $ days. That is, $ a_i $ — is the estimated air temperature on day $ i $ ( $ 1 \le i \le n $ ). You are also given an array $ b $ — the air temperature that was actually present on each of the days. However, all the values in array $ b $ are mixed up. Determine which day was which temperature, if you know that the weather never differs from the forecast by more than $ k $ degrees. In other words, if on day $ i $ the real air temperature was $ c $ , then the equality $ |a_i - c| \le k $ is always true. For example, let an array $ a $ = \[ $ 1, 3, 5, 3, 9 $ \] of length $ n = 5 $ and $ k = 2 $ be given and an array $ b $ = \[ $ 2, 5, 11, 2, 4 $ \]. Then, so that the value of $ b_i $ corresponds to the air temperature on day $ i $ , we can rearrange the elements of the array $ b $ so: \[ $ 2, 2, 5, 4, 11 $ \]. Indeed: - On the $ 1 $ st day, $ |a_1 - b_1| = |1 - 2| = 1 $ , $ 1 \le 2 = k $ is satisfied; - On the $ 2 $ nd day $ |a_2 - b_2| = |3 - 2| = 1 $ , $ 1 \le 2 = k $ is satisfied; - On the $ 3 $ rd day, $ |a_3 - b_3| = |5 - 5| = 0 $ , $ 0 \le 2 = k $ is satisfied; - On the $ 4 $ th day, $ |a_4 - b_4| = |3 - 4| = 1 $ , $ 1 \le 2 = k $ is satisfied; - On the $ 5 $ th day, $ |a_5 - b_5| = |9 - 11| = 2 $ , $ 2 \le 2 = k $ is satisfied.

The first line of input data contains a single integer $ t $ ( $ 1 \le t \le 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 $ ( $ 1 \le n \le 10^5 $ ) and $ k $ ( $ 0 \le k \le10^9 $ ) — the number of days and the maximum difference between the expected and actual air temperature on each day. The second line of each test case contains exactly $ n $ integers — elements of array $ a $ ( $ -10^9 \le a_i \le 10^9 $ ). The third line of each test case contains exactly $ n $ integers — elements of array $ b $ ( $ -10^9 \le b_i \le 10^9 $ ). It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 10^5 $ , and that the elements of array $ b $ can always be rearranged so that the equality $ |a_i - b_i| \le k $ is true for all $ i $ .

On a separate line for each test case, output exactly $ n $ numbers — the values of air temperature on each of the days in the correct order. If there is more than one answer — output any of them.