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;
int main() {
  int t;
  cin >> t;
  while (t--) {
    int n, d;
    cin >> n >> d;
    int ub = n * (n - 1) / 2;
    int lb = 0;
    int cur = 0;
    for (int i = 1; i <= n; ++i) {
      if (!(i & (i - 1))) {
        cur++;
      }
      lb += cur - 1;
    }
    if (d < lb || d > ub) {
      puts("NO");
      continue;
    }
    vector<int> par(n);
    iota(par.begin(), par.end(), -1);
    vector<int> n_ch(n, 1);
    n_ch[n - 1] = 0;
    vector<int> depth(n);
    iota(depth.begin(), depth.end(), 0);
    int right = n;
    while (d < ub) {
      int v = 0;
      for (int i = 0; i < right; ++i) {
        if (n_ch[i] == 0) {
          v = i;
        }
      }
      bool found = false;
      bool stop = false;
      for (int i = n - 1; i >= 0; --i) {
        if (depth[v] - depth[i] == 2 && n_ch[i] < 2) {
          n_ch[par[v]]--;
          par[v] = i;
          n_ch[i]++;
          depth[v]--;
          ub--;
          found = true;
          if (ub <= d) {
            stop = true;
            break;
          }
        }
      }
      if (!found) right--;
      if (stop) {
        break;
      }
    }
    puts("YES");
    for (int i = 1; i < n; ++i) {
      cout << par[i] + 1;
      if (i == n - 1)
        puts("");
      else
        cout << ' ';
    }
  }
  return 0;
}