Codeforces Round 874 (Div. 3) |
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B. Restore the Weather

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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

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

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.

Example

Input

35 21 3 5 3 92 5 11 2 46 1-1 3 -2 0 -5 -1-4 0 -1 4 0 03 37 7 79 4 8

Output

2 2 5 4 11 0 4 -1 0 -4 0 8 4 9

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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