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 ld = 0;
    int cd = 0;
    int rd = (n * (n - 1)) / 2;
    for (int i = 1; i <= n; i++) {
      if (!(i & (i - 1))) ++cd;
      ld += cd - 1;
    }
    if (!(ld <= d && d <= rd)) {
      cout << "NO" << endl;
      continue;
    }
    vector<int> par(n);
    iota(par.begin(), par.end(), -1);
    vector<int> cnt(n, 1);
    cnt[n - 1] = 0;
    vector<int> bad(n);
    vector<int> depth(n);
    iota(depth.begin(), depth.end(), 0);
    int cur = (n * (n - 1)) / 2;
    while (cur > d) {
      int v = -1;
      for (int i = 0; i < n; i++) {
        if (bad[i] == 0 && cnt[i] == 0 && (v == -1 || depth[v] > depth[i])) {
          v = i;
        }
      }
      int p = -1;
      for (int i = 0; i < n; i++) {
        if (cnt[i] < 2 && depth[i] < depth[v] - 1 &&
            (p == -1 || depth[i] > depth[p])) {
          p = i;
        }
      }
      if (p == -1) {
        bad[v] = 1;
        continue;
      }
      assert(depth[v] - depth[p] == 2);
      --cnt[par[v]];
      ++cnt[p];
      --depth[v];
      par[v] = p;
      --cur;
    }
    cout << "YES" << endl;
    for (int i = 1; i < n; i++) {
      cout << par[i] + 1 << " ";
    }
    cout << endl;
  }
}