E. Construct the Binary Treetime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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).OutputFor 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.ExampleInput
3
5 7
10 19
10 18
Output
YES
1 2 1 3 
YES
1 2 3 3 9 9 2 1 6 
NO
NotePictures corresponding to the first and the second test cases of the example:
3
5 7
10 19
10 18

YES 1 2 1 3  YES 1 2 3 3 9 9 2 1 6  NO 
['brute force', 'constructive algorithms', 'trees', '*2200']