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.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.*;

public class ProblemE_New {

    public static InputStream inputStream = System.in;

    public static OutputStream outputStream = System.out;

    public static void main(String[] args) {
        Scanner scanner = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);

        int t = scanner.nextInt();
        for (int p = 0; p < t; p++) {
            int n = scanner.nextInt();
            int d = scanner.nextInt();

            if (d > n * (n - 1) / 2) {
                out.println("NO");
                continue;
            }

            d = n * (n - 1) / 2 - d;

            int[] ans = new int[n + 1];
            Map<Integer, LinkedList<Integer>> map = new HashMap<>();
            for (int i = 1; i <= n; i++) {
                map.put(i - 1, new LinkedList<>());
                map.get(i - 1).add(i);
                ans[i] = i -1;
            }
            int minPossibleDepth = 0;

            for (int i = n; i >= 0; i--) {
                int change = Math.min(d, (i - 2 - minPossibleDepth));
                int index = i - 2 - change;
                int x = map.get(index).poll();
                ans[i] = x;
                map.get(index + 1).add(i);
                map.get(index + 1).add(i);
                if (map.get(index).size() == 0) {
                    minPossibleDepth++;
                }
                d -= change;
                if (d == 0) {
                    break;
                }
            }

            if (d == 0) {
                out.println("YES");
                for (int i = 2; i <= n; i++) {
                    out.print(ans[i] + " ");
                }
                out.println();
            } else {
                out.println("NO");
            }

        }
        out.flush();
    }
}