You are given two integers $n$ and $d$. You need to construct a rooted binary tree consisting of $n$ vertices with a root at the vertex $1$ and the sum of depths of all vertices equals to $d$.

A tree is a connected graph without cycles. A rooted tree has a special vertex called the root. A parent of a vertex $v$ is the last different from $v$ vertex on the path from the root to the vertex $v$. The depth of the vertex $v$ is the length of the path from the root to the vertex $v$. Children of vertex $v$ are all vertices for which $v$ is the parent. The binary tree is such a tree that no vertex has more than $2$ children.

You have to answer $t$ independent test cases.

Input

The first line of the input contains one integer $t$ ($1 \le t \le 1000$) — the number of test cases.

The only line of each test case contains two integers $n$ and $d$ ($2 \le n, d \le 5000$) — the number of vertices in the tree and the required sum of depths of all vertices.

It is guaranteed that the sum of $n$ and the sum of $d$ both does not exceed $5000$ ($\sum n \le 5000, \sum d \le 5000$).

Output

For each test case, print the answer.

If it is impossible to construct such a tree, print "NO" (without quotes) in the first line. Otherwise, print "{YES}" in the first line. Then print $n-1$ integers $p_2, p_3, \dots, p_n$ in the second line, where $p_i$ is the parent of the vertex $i$. Note that the sequence of parents you print should describe some binary tree.

见题面 Input 部分

见题面 Output 部分

Pictures corresponding to the first and the second test cases of the example: