Restore the Weather
Contest: Codeforces Round 874 (Div. 3)
Difficulty rating: 900
Tags: greedy, sortings

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.

Input format:
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 $$$i$$$.

Output format:
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.

Constraints:
Time limit: 1.0 s
Memory limit: 256.0 MB

Example input:
3
5 2
1 3 5 3 9
2 5 11 2 4
6 1
-1 3 -2 0 -5 -1
-4 0 -1 4 0 0
3 3
7 7 7
9 4 8

Example output:
2 2 5 4 11
0 4 -1 0 -4 0
8 4 9

Editorial:
Let's solve the problem using a greedy algorithm.
Based on the array $$$a$$$, form an array of pairs {temperature, day number} and sort it in ascending order of temperature. Also sort the array $$$b$$$ in ascending order. Now, the values $$$a[i].first$$$ and $$$b[i]$$$ are the predicted and real temperature on day $$$a[i].second$$$.
Indeed, consider the minimum temperatures $$$b[1]$$$ and $$$a[1].first$$$. The difference between them is $$$t = |b[1] - a[1].first|$$$. If we consider the value $$$|b[i] - a[1].first|$$$ or $$$|b[1] - a[i].first|$$$ at $$$i \gt 1$$$, there will be at least $$$t$$$ since $$$a[1] \le a[i]$$$ and $$$b[1] \le b[i]$$$.
Since it is guaranteed that it is possible to rearrange the elements in the array $$$b$$$, and the elements $$$b[1]$$$ and $$$a[1].first$$$ have the smallest difference, it is definitely not greater than $$$k$$$.