Problem Statement

You are given positive integers $M,K$.

Determine whether there exist a positive integer $N$ and an integer sequence $A=(A_1,A_2,\ldots, A_N)$ that satisfy all the following conditions, and if they exist, find one.

• $1\le N\le M$
• $0\le A_i < M$ $(1\le i\le N)$
• There are exactly $K$ integers $0\le k < M$ such that there exists a pair of indices $(i,j)$ satisfying $k\equiv A_i+A_j \pmod M$.

You are given $T$ test cases, so find the answer for each.

Constraints

• $1\le T\le 2\times 10^5$
• $1\le K\le M\le 2\times 10^5$
• The sum of $M$ over all test cases is at most $2\times 10^5$.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

T
\text{case}_1
\text{case}_2
\vdots
\text{case}_T

Each test case is given in the following format:

M K

Output

Output your solutions for the test cases in order, separated by newlines.

For each test case, if there are no $N,A$ that satisfy all conditions, output No.

Otherwise, output $N$ and $A$ that satisfy all conditions in the following format:

Yes
N
A_1 A_2 \ldots A_N

If there are multiple $N$ and $A$ that satisfy the conditions, you may output any of them.