- Prepare
- Algorithms
- Implementation
- Absolute Permutation

# Absolute Permutation

# Absolute Permutation

We define to be a permutation of the first natural numbers in the range . Let denote the value at position in permutation using -based indexing.

is considered to be an *absolute permutation* if holds true for every .

Given and , print the lexicographically smallest absolute permutation . If no absolute permutation exists, print `-1`

.

**Example**

Create an array of elements from to , . Using based indexing, create a permutation where every . It can be rearranged to so that all of the absolute differences equal :

pos[i] i |pos[i] - i| 3 1 2 4 2 2 1 3 2 2 4 2

**Function Description**

Complete the *absolutePermutation* function in the editor below.

absolutePermutation has the following parameter(s):

*int n:*the upper bound of natural numbers to consider, inclusive*int k:*the absolute difference between each element's value and its index

**Returns**

*int[n]:*the lexicographically smallest permutation, or if there is none

**Input Format**

The first line contains an integer , the number of queries.

Each of the next lines contains space-separated integers, and .

**Constraints**

**Sample Input**

STDIN Function ----- -------- 3 t = 3 (number of queries) 2 1 n = 2, k = 1 3 0 n = 3, k = 0 3 2 n = 3, k = 2

**Sample Output**

```
2 1
1 2 3
-1
```

**Explanation**

*Test Case 0:*

*Test Case 1:*

*Test Case 2:*

No absolute permutation exists, so we print `-1`

on a new line.