Description

Input

Each test consists of multiple test cases. The first line contains a single integer $t$ ($1 \leq t \leq 10^{4}$) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers $n$ and $k$ ($1 \le n \le 2 \cdot 10^{5}, 0 \le k \le 10^{12}$) — the length of the permutation and the required Manhattan value.

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 permutation, output "No". Otherwise, in the first line, output "Yes", and in the second line, output $n$ distinct integers $p_1, p_2, \ldots, p_n$ ($1 \le p_i \le n$) — a suitable permutation.

If there are multiple solutions, output any of them.

You can output the answer in any case (for example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as a positive answer).

8
3 4
4 5
7 0
1 1000000000000
8 14
112 777
5 12
5 2
 
 
 
 

Yes
3 1 2
No
Yes
1 2 3 4 5 6 7
No
Yes
8 2 3 4 5 6 1 7
No
Yes
5 4 3 1 2
Yes
2 1 3 4 5

Note

In the first test case, the permutation $[3, 1, 2]$ is suitable, its Manhattan value is $|3 - 1| + |1 - 2| + |2 - 3| = 2 + 1 + 1 = 4$.

In the second test case, it can be proven that there is no permutation of length $4$ with a Manhattan value of $5$.

In the third test case, the permutation $[1,2,3,4,5,6,7]$ is suitable, its Manhattan value is $|1-1|+|2-2|+|3-3|+|4-4|+|5-5|+|6-6|+|7-7|=0$.