absolute-permutation

Absolute Permutation ⬀

We define P to be a permutation of the first n natural numbers in the range [1, n]. Let pos[i] denote the value at position i in permutation P using 1-based indexing.

P is considered to be an absolute permutation if |pos[i] - i| = k holds true for every i ∈ [1, n].

Given n and k, print the lexicographically smallest absolute permutation P. If no absolute permutation exists, print -1.

Example

• n = 4
• k = 2

Create an array of elements from 1 to n, pos = [1, 2, 3, 4]. Using 1 based indexing, create a permutation where every |pos[i] - i| = k. It can be rearranged to [3, 4, 1, 2] so that all of the absolute differences equal k = 2:

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 [-1] if there is none

Input Format

• The first line contains an integer t, the number of queries.
• Each of the next t lines contains 2 space-separated integers, n and k.

Constraints

• 1 ≤ t < 10
• 1 ≤ n ≤ 10⁵
• 0 ≤ k < n

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.