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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int inf = 0x3f3f3f3f, maxn = 5010;
int pre[maxn], dep[maxn], node[maxn];
bool flag[maxn];
int main() {
  int t;
  cin >> t;
  while (t--) {
    memset(flag, false, sizeof flag);
    int n, d;
    cin >> n >> d;
    int maxd = 0;
    node[0] = 1;
    for (int i = 2; i <= n; i++) {
      pre[i] = i / 2;
      dep[i] = dep[pre[i]] + 1;
      d -= dep[i];
      maxd = max(maxd, dep[i]);
    }
    if (d < 0) {
      cout << "NO\n";
      continue;
    }
    int idx = n;
    while (idx) {
      node[dep[idx]] = idx;
      flag[idx] = true;
      idx = pre[idx];
    }
    for (int i = n; i >= 1; i--) {
      if (flag[i]) continue;
      int tmp = maxd;
      while (dep[pre[i]] < tmp && d) {
        pre[i] = node[dep[i]];
        dep[i]++;
        if (dep[i] > maxd) {
          maxd++;
          node[maxd] = i;
          flag[i] = 1;
        }
        d--;
      }
    }
    if (d) {
      cout << "NO\n";
      continue;
    }
    cout << "YES\n";
    for (int i = 2; i <= n; i++) {
      cout << pre[i] << " ";
    }
    cout << "\n";
  }
  return 0;
}