Description：
You are given two integers nnn and ddd. You need to construct a rooted binary tree consisting of n vertices with a root at the vertex 111 and the sum of depths of all vertices equals to ddd.
A tree is a connected graph without cycles. A rooted tree has a special vertex called the root. A parent of a vertex vvv is the last different from v vertex on the path from the root to the vertex v. The depth of the vertex vvv is the length of the path from the root to the vertex vvv. 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 222 children.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t(1≤t≤1000)t (1≤t≤1000)t(1≤t≤1000) — the number of test cases.
The only line of each test case contains two integers nnn and d(2≤n,d≤5000)d (2≤n,d≤5000)d(2≤n,d≤5000)— the number of vertices in the tree and the required sum of depths of all vertices.
It is guaranteed that the sum of nnn and the sum of ddd both does not exceed 500050005000 (∑n≤5000,∑d≤5000)(∑n≤5000,∑d≤5000)(∑n≤5000,∑d≤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 p2,p3,…,pn in the second line, where pi is the parent of the vertex i. Note that the sequence of parents you print should describe some binary tree.
Example
input
3
5 7
10 19
10 18
1
2
3
4
output
YES
1 2 1 3
YES
1 2 3 3 9 9 2 1 6
NO
1
2
3
4
5
Note
Pictures corresponding to the first and the second test cases of the example:
思路
給定t組數據，每組數據限定n個結點和深度和d
求能否構成二叉樹且節點深度和是否等於d
滿足並輸出每個節點的深度
首先節點全在一條分支上深度和最大，然後在此狀態上將後面的點前移動
，每次移動更新完判斷是否能夠滿足條件
進行構造即可