Let f be a [permutation] of length N, where N is even. The riffle of f is defined to be the permutation
$g = (f(1), f(3), \ldots, f(N-1), f(2), f(4), \ldots, f(N))$

You are given two integers N and K. Output the resultant permutation when you riffle the identity permutation of length N, K times.

The identity permutation of length N is ${\sigma}_N = (1, 2, \ldots, N)$

------ Input Format ------

• The first line of input contains a single integer T, denoting the number of test cases. The description of T test cases follows.
• Each test case consists of a single line of input, containing two space-separated integers N and K.

------ Output Format ------

For each test case, output the answer permutation as N space-separated integers in a new line.

------ Constraints ------

$1 ≤ T ≤ 100$
$1 ≤ N ≤ 3 \cdot 10^{5}$
$1 ≤ K ≤ 10^{9}$
$N$ is even
- The sum of $N$ across test cases does not exceed $3 \cdot 10^{5}$

------ subtasks ------

Subtask 1 (30 points): $N$ is a power of $2$
Subtask 2 (70 points): Original constraints

----- Sample Input 1 ------
3
6 1
8 2
14 452
----- Sample Output 1 ------
1 3 5 2 4 6
1 5 2 6 3 7 4 8
1 10 6 2 11 7 3 12 8 4 13 9 5 14
----- explanation 1 ------
Test case $1$: Performing the riffle on $\sigma_{6} = (1, 2, 3, 4, 5, 6)$ once results in $(1, 3, 5, 2, 4, 6)$, by definition.

Test case $2$: The process goes as follows:
- Performing the riffle on $(1, 2, 3, 4, 5, 6, 7, 8)$ results in $(1, 3, 5, 7, 2, 4, 6, 8)$
- Performing the riffle on $(1, 3, 5, 7, 2, 4, 6, 8)$ results in $(1, 5, 2, 6, 3, 7, 4, 8)$

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