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:
import sys
input = sys.stdin.readline

t=int(input())

for tests in range(t):
    n,d=map(int,input().split())
    MIN=sum([i.bit_length()-1 for i in range(1,n+1)])
    MAX=(n-1)*n//2

    if MIN<=d<=MAX:
        print("YES")
    else:
        print("NO")
        continue

    TREE=[i//2 for i in range(n+1)]
    STEM=[1<<i for i in range(n.bit_length())]
    SETSTEM=set(STEM)
   
    rest=d-MIN

    #print(TREE,STEM,rest)

    for x in range(n,-1,-1):
        if x in SETSTEM:
            continue
        if rest==0:
            break

        now_height=x.bit_length()-1
        max_height=len(STEM)

        #print(x,now_height,max_height)

        if rest>max_height-now_height:
            rest-=max_height-now_height
            TREE[x]=STEM[-1]
            STEM.append(x)

        else:
            TREE[x]=STEM[now_height+rest-1]
            break

    print(*TREE[2:])