CSES - Monotone Subsequences
  • Time limit: 1.00 s
  • Memory limit: 512 MB

Your task is to create a permutation of numbers 1,2,,n1,2,\dots,n whose longest monotone subsequence has exactly kk elements.

A monotone subsequence is either increasing or decreasing. For example, some monotone subsequences in [2,1,4,5,3][2,1,4,5,3] are [2,4,5][2,4,5] and [4,3][4,3].

Input

The first input line has an integer tt: the number of tests.

After this, there are tt lines. Each line has two integers nn and kk.

Output

For each test, print a line that contains the permutation. You can print any valid solution. If there are no solutions, print IMPOSSIBLE.

Constraints

  • 1t10001 \le t \le 1000
  • 1kn1001 \le k \le n \le 100

Example

Input:

3
5 3
5 2
7 7

Output:

2 1 4 5 3
IMPOSSIBLE
1 2 3 4 5 6 7