You are given a positive integer $N$ and a nonnegative integer $X$.

Determine whether there exists a sequence $A = (A_1, A_2, \dots, A_{2N})$ of length $2N$ satisfying all of the following conditions.

• Each integer from $1$ to $N$ appears in $A$ exactly twice.
• The sequence $(1, 2, \dots, N)$ occurs exactly $X$ times as a subsequence of $A$. In other words, there are exactly $X$ ways to choose indices $1 \le i_1 < i_2 < \dots < i_N \le 2N$ such that $A_{i_j} = j$ $(1 \le j \le N)$.

If such a sequence exists, output one. If multiple such sequences exist, output any one of them.

Input

The input consists of multiple test cases in the following format.

$$ \begin{aligned} &T \\ &\mathrm{case}_1 \\ &\mathrm{case}_2 \\ &\vdots \\ &\mathrm{case}_T \end{aligned} $$

Each test case is given in the following format.

$$ N \ X $$

The first line contains an integer $T$ $(1 \le T \le 2 \times 10^5)$, the number of test cases.

For each test case, you are given a positive integer $N$ $(1 \le N \le 2 \times 10^5)$ and a nonnegative integer $X$ $(0 \le X \le 10^{18})$.

The sum of $N$ over all test cases does not exceed $2 \times 10^5$.

Output

For each test case, if there is no sequence satisfying the conditions, print No on a single line.

Otherwise, print Yes on the first line, and print $2N$ integers $A_1, A_2, \dots, A_{2N}$ representing a sequence satisfying the conditions on the second line.

If there are multiple valid sequences, you may output any of them.

Example

Input 1

3
2 3
50 1000000000000000000
4 0

Output 1

Yes
1 2 1 2
No
Yes
4 4 3 3 2 2 1 1