Monotone Subsequences

Your task is to create a permutation of numbers 1,2,\dots,n whose longest monotone subsequence has exactly k elements. A monotone subsequence is either increasing or decreasing. For example, some monotone subsequences in [2,1,4,5,3] are [2,4,5] and [4,3].

Input

The first input line has an integer t: the number of tests. After this, there are t lines. Each line has two integers n and k.

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

$1 \le t \le 1000$

$1 \le k \le n \le 100$

Example

Input

3
5 3
5 2
7 7

Output

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