Divisible Sum Pairing

You are given two arrays arr1 and arr2 of equal length and an integer k. Your task is to rearrange arr2 (i.e. find a permutation) such that for each index i the sum arr1[i] + arr2[i] is divisible by k. If such a permutation exists, print the resulting pairs. Otherwise, print None.

Note: Each valid pair is printed as two numbers separated by a space on a new line. You must read input from stdin and output your answer to stdout.

Mathematically, for the found permutation p of indices, it must satisfy: $$ \forall\,i,\quad \; (arr1[i] + p(arr2)[i])\, \%\, k = 0. $$

inputFormat

The input consists of four lines:

1. An integer n representing the number of elements in each array.
2. n space-separated integers representing arr1.
3. n space-separated integers representing arr2.
4. An integer k, the divisor.

outputFormat

If a valid reordering of arr2 exists such that arr1[i] + arr2[i] is divisible by k for every index i, print each pair in a new line as a b (where a is from arr1 and b from the corresponding position in the rearranged arr2). If there is no valid pairing, print None.

## sample

4
1 2 3 4
4 3 2 1
5

1 4
2 3
3 2
4 1

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