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.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class ProblemE {

    static class Node {
        int index;
        int level;
        int parent;
        Node left;
        Node right;

        Node(int index, int level, int parent) {
            this.index = index;
            this.level = level;
            this.parent = parent;
        }
    }

    static List<Integer> solve(int n, int d) {
        int sum = n * (n - 1) / 2;
        if (sum < d) {
            return null;
        }
        Node[] nodes = new Node[n];
        List<List<Node>> vacant = new ArrayList<>();
        Node root = new Node(0, 0, -1);
        nodes[0] = root;
        vacant.add(new ArrayList<>());
        vacant.get(0).add(root);
        for (int i = 1; i < n; i++) {
            nodes[i] = new Node(i, i, i - 1);
            nodes[i - 1].left = nodes[i];
            vacant.add(new ArrayList<>());
            vacant.get(i).add(nodes[i]);
        }
        Node bottom = nodes[n - 1];
        int topVacant = 0;
        while (sum > d && bottom.level > topVacant + 1) {
            int maxUp = bottom.level - (topVacant + 1);
            int newLevel = topVacant;
            if (sum - maxUp < d) {
                newLevel = bottom.level - (sum - d) - 1;
            }
            Node oldParent = nodes[bottom.parent];
            List<Node> levelNodes = vacant.get(newLevel);
            Node newParent = levelNodes.get(levelNodes.size() - 1);
            if (newParent.left != null) {
                newParent.right = bottom;
                levelNodes.remove(levelNodes.size() - 1);
            } else {
                newParent.left = bottom;
            }
            oldParent.left = null;
            bottom.parent = newParent.index;
            bottom.level = newParent.level + 1;
            vacant.get(bottom.level).add(bottom);
            bottom = oldParent;
            sum -= oldParent.level - newParent.level;
            while (vacant.get(topVacant).isEmpty()) {
                topVacant++;
            }
        }
        if (sum != d) {
            return null;
        } else {
            List<Integer> answer = new ArrayList<>();
            for (int i = 1; i < n; i++) {
                answer.add(nodes[i].parent + 1);
            }
            return answer;
        }
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while (t > 0) {
            int n = sc.nextInt();
            int d = sc.nextInt();
            List<Integer> answer = solve(n, d);
            if (answer == null) {
                System.out.println("NO");
            } else {
                System.out.println("YES");
                for (int i : answer) {
                    System.out.print(i + " ");
                }
                System.out.println();
            }
            t--;
        }
    }
}