You are given an array $$$a = [1, 2, \ldots, n]$$$, where $$$n$$$ is odd, and an integer $$$k$$$.

Your task is to choose an odd positive integer $$$m$$$ and to split $$$a$$$ into $$$m$$$ subarrays$$$^{\dagger}$$$ $$$b_1, b_2, \ldots, b_m$$$ such that:

Each element of the array $$$a$$$ belongs to exactly one subarray.
For all $$$1 \le i \le m$$$, $$$|b_i|$$$ is odd, i.e., the length of each subarray is odd.
$$$\operatorname{median}([\operatorname{median}(b_1), \operatorname{median}(b_2), \ldots, \operatorname{median}(b_m)]) = k$$$, i.e., the median$$$^{\ddagger}$$$ of the array of medians of all subarrays must equal $$$k$$$. $$$\operatorname{median}(c)$$$ denotes the median of the array $$$c$$$.

$$$^{\dagger}$$$A subarray of the array $$$a$$$ of length $$$n$$$ is the array $$$[a_l, a_{l + 1}, \ldots, a_r]$$$ for some integers $$$1 \le l \le r \le n$$$.

$$$^{\ddagger}$$$A median of the array of odd length is the middle element after the array is sorted in non-decreasing order. For example: $$$\operatorname{median}([1,2,5,4,3]) = 3$$$, $$$\operatorname{median}([3,2,1]) = 2$$$, $$$\operatorname{median}([2,1,2,1,2,2,2]) = 2$$$.

Input

Each test consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 5000$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le k \le n \lt 2 \cdot 10^5$$$, $$$n$$$ is odd) — the length of array $$$a$$$ and the desired median of the array of medians of all subarrays.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case:

If there is no suitable partition, output $$$-1$$$ in a single line.
Otherwise, in the first line, output an odd integer $$$m$$$ ($$$1 \le m \le n$$$), and in the second line, output $$$m$$$ distinct integers $$$p_1, p_2 , p_3 , \ldots, p_m$$$ ($$$1 = p_1 \lt p_2 \lt p_3 \lt \ldots \lt p_m \le n$$$) — denoting the left borders of each subarray.

In detail, for a valid answer $$$[p_1, p_2, \ldots, p_m]$$$:

$$$b_1 = \left[ a_{p_1}, a_{p_1 + 1}, \ldots, a_{p_2 - 1} \right]$$$
$$$b_2 = \left[ a_{p_2}, a_{p_2 + 1}, \ldots, a_{p_3 - 1} \right]$$$
$$$\ldots$$$
$$$b_m = \left[ a_{p_m}, a_{p_m + 1}, \ldots, a_n \right]$$$.

If there are multiple solutions, you can output any of them.

Note

In the first test case, the given partition has $$$m = 1$$$ and $$$b_1 = [1]$$$. It is obvious that $$$\operatorname{median}([\operatorname{median}([1])]) = \operatorname{median}([1]) = 1$$$.

In the second test case, the given partition has $$$m = 3$$$ and:

$$$b_1 = [1]$$$
$$$b_2 = [2]$$$
$$$b_3 = [3]$$$

Therefore, $$$\operatorname{median}([\operatorname{median}([1]), \operatorname{median}([2]), \operatorname{median}([3])]) = \operatorname{median}([1, 2, 3]) = 2$$$.

In the third test case, there is no valid partition for $$$k = 3$$$.

In the fourth test case, the given partition has $$$m = 5$$$ and:

$$$b_1 = [1, 2, 3]$$$
$$$b_2 = [4, 5, 6]$$$
$$$b_3 = [7, 8, 9]$$$
$$$b_4 = [10, 11, 12]$$$
$$$b_5 = [13, 14, 15]$$$

Therefore, $$$\operatorname{median}([\operatorname{median}([1, 2, 3]), \operatorname{median}([4, 5, 6]), \operatorname{median}([7, 8, 9]), \operatorname{median}([10, 11, 12]), \operatorname{median}([13, 14, 15])]) = \operatorname{median}([2, 5, 8, 11, 14]) = 8$$$.

Medians

Examples