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() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int TESTS = 1;
  cin >> TESTS;
  while (TESTS--) {
    long long n, d;
    cin >> n >> d;
    vector<long long> con(n, 1);
    long long l = 1;
    long long r = n - 1;
    long long h = (n * (n - 1)) / 2;
    h -= d;
    while (l < r) {
      while (l < r && ((h - r + l) < 0 || con[l] + 1 > 2 * con[l - 1])) l++;
      if (l >= r) break;
      h += l;
      h -= r;
      con[l]++;
      con[r]--;
      r--;
    }
    if (h != 0) {
      cout << "NO" << endl;
      continue;
    }
    cout << "YES" << endl;
    std::vector<long long> pref;
    pref.push_back(0);
    for (long long i = 0; i < n; i++) {
      pref.push_back(pref[i] + con[i]);
    }
    for (long long i = 1; i < n; i++) {
      for (long long j = 0; j < con[i]; j++) {
        cout << pref[i - 1] + 1 + j / 2 << " ";
      }
    }
    cout << endl;
  }
  return 0;
}