Problem: 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 ≤ 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 (∑ 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 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.

Example

Input


3
5 7
10 19
10 18


Output


YES
1 2 1 3 
YES
1 2 3 3 9 9 2 1 6 
NO

Note

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

<image>

<image>

Solution (in PYTHON3):

Solution:


t = int(input())
for _ in range(t):
    n,d = map(int,input().split())

    dsum = n*(n-1)//2

    if d>dsum: 
        print("NO")
        continue

    tree = [[i] for i in range(n)]

    lmin = 1
    while dsum > d:
        l = len(tree)-1
        while dsum > d and l>lmin:
            l -= 1
            dsum -= 1

        if l == len(tree)-1:
            break

        node = tree[-1][-1]
        tree[-1].pop()
        if not tree[-1]:
            tree.pop()
        tree[l].append(node)
        if len(tree[l])==2**l:
            lmin += 1

    
    if dsum > d:
        print("NO")
        continue
    
    print("YES")
    parent = [0]*(n-1)
    for j in range(1,len(tree)):
        layer = tree[j]
        for i in range(len(layer)):
            node = layer[i]
            parent[node-1] = tree[j-1][i//2] + 1

    print(*parent)