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