# Restore the Weather solution codeforces

## Restore the Weather solution codeforces

You are given an array 𝑎 containing the weather forecast for Berlandia for the last 𝑛 days. That is, 𝑎𝑖�� — is the estimated air temperature on day 𝑖 (1𝑖𝑛1≤�≤�).

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 |𝑎𝑖𝑐|𝑘|��−�|≤� is always true.

For example, let an array 𝑎 = [1,3,5,3,91,3,5,3,9] of length 𝑛=5�=5 and 𝑘=2�=2 be given and an array 𝑏 = [2,5,11,2,42,5,11,2,4]. Then, so that the value of 𝑏𝑖�� corresponds to the air temperature on day 𝑖, we can rearrange the elements of the array 𝑏 so: [2,2,5,4,112,2,5,4,11]. Indeed:

• On the 11st day, |𝑎1𝑏1|=|12|=1|�1−�1|=|1−2|=112=𝑘1≤2=� is satisfied;
• On the 22nd day |𝑎2𝑏2|=|32|=1|�2−�2|=|3−2|=112=𝑘1≤2=� is satisfied;
• On the 33rd day, |𝑎3𝑏3|=|55|=0|�3−�3|=|5−5|=002=𝑘0≤2=� is satisfied;
• On the 44th day, |𝑎4𝑏4|=|34|=1|�4−�4|=|3−4|=112=𝑘1≤2=� is satisfied;
• On the 55th day, |𝑎5𝑏5|=|911|=2|�5−�5|=|9−11|=222=𝑘2≤2=� is satisfied.

## Restore the Weather solution codeforces

The first line of input data contains a single integer 𝑡 (1𝑡1041≤�≤104) — the number of test cases.

The description of the test cases follows.

The first line of each test case contains two integers 𝑛 (1𝑛1051≤�≤105) and 𝑘 (0𝑘1090≤�≤109) — 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 (109𝑎𝑖109−109≤��≤109).

The third line of each test case contains exactly 𝑛 integers — elements of array 𝑏 (109𝑏𝑖109−109≤��≤109).

It is guaranteed that the sum of 𝑛 over all test cases does not exceed 105105, and that the elements of array 𝑏 can always be rearranged so that the equality |𝑎𝑖𝑏𝑖|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

Copy
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
output

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