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 JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.PriorityQueue;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Jaynil
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        EConstructTheBinaryTree solver = new EConstructTheBinaryTree();
        int testCount = Integer.parseInt(in.next());
        for (int i = 1; i <= testCount; i++)
            solver.solve(i, in, out);
        out.close();
    }

    static class EConstructTheBinaryTree {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int d = in.nextInt();
            int tot = (n * (n - 1)) / 2;
            PriorityQueue<int[]> highest = new PriorityQueue<>((x, y) -> x[1] - y[1]);
            PriorityQueue<int[]> lowest = new PriorityQueue<>((x, y) -> y[1] - x[1]);
            if (d > tot) {
                out.println("NO");
                return;
            }
            //p d c
            int a[][] = new int[n][4];
            for (int i = 0; i < n; i++) {
                a[i][0] = i - 1;
                a[i][1] = i;
                a[i][2] = 1;
                a[i][3] = i;
                highest.add(a[i]);
                lowest.add(a[i]);
            }
            a[n - 1][2] = 0;
            while (highest.size() > 0 && lowest.size() > 0 && tot - d > 0) {
                int[] h = highest.poll();
                if (h[2] == 2) continue;
                int[] l = lowest.poll();
                if (l[2] > 0) {
                    highest.add(h);
                    continue;
                }
                if (tot - l[1] + 1 + h[1] >= d) {
                    tot = tot - l[1] + 1 + h[1];
                    h[2]++;
                    a[l[0]][2]--;
                    l[1] = h[1] + 1;
                    l[0] = h[3];
                    highest.add(l);
                    highest.add(h);
                } else {
                    lowest.add(l);
                }
            }
            if (tot == d) {
                out.println("YES");
                for (int i = 1; i < n; i++) {
                    out.print((a[i][0] + 1) + " ");
                }
                out.println();
            } else {
                out.println("NO");
//            out.println(tot);
//            out.println(highest.size());
//            out.println(lowest.size());
//            for(int i=1;i<n;i++){
//                out.print((a[i][0]+1) + " ");
//            }
                out.println();
            }
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}