B'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. The first line of the input contains one integer t ( 1 <= t <= 1000 ) -- the number of test cases. The only line of each test case contains two integers n and 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 n and the sum of d both does not exceed 5000 ( sum n <= 5000, sum d <= 5000 ). 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, ... , 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. Pictures corresponding to the first and the second test cases of the example: '...