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:
//package com.kraken.cf.cf624;
/*
 * Author: Kraken
 * Created on 3/1/2020 at 4:09 AM
 */

import java.io.*;
import java.util.*;

public class E {

	public static void main(String[] args) {
		FastReader sc = new FastReader();
		int t = sc.nextInt();
		while (t-- > 0) {
			int n = sc.nextInt();
			int d = sc.nextInt();

			int lb = 0, sum = (n * (n - 1)) / 2;
			for (int i = 1, cd = 0; i <= n; i++) {
				if ((i & (i-1)) == 0) cd++;
				lb += cd - 1;
			}
			if (d > sum || d < lb) {
				System.out.println("NO");
				continue;
			}

			boolean[] bad = new boolean[n];
			Arrays.fill(bad, false);
			int[] res = new int[n];
			for (int i = 0, k = -1; i < n; i++, k++) res[i] = k;
			int[] cnt = new int[n];
			Arrays.fill(cnt, 1);
			cnt[n - 1] = 0;
			int[] depth = new int[n];
			for (int i = 0; i < n; i++) depth[i] = i;

			while (sum > d) {
				int v = -1;
				for (int i = 0; i < n; i++) {
					if (!bad[i] && cnt[i] == 0 && (v == -1 || depth[v] > depth[i])) {
						v = i;
					}
				}

				if (v == -1) {
					System.out.println("NO");
					return;
				}

				int p = -1;
				for (int i = 0; i < n; i++) {
					if (cnt[i] < 2 && depth[i] < depth[v] - 1 && (p == -1 || depth[p] < depth[i])) {
						p = i;
					}
				}

				if (p == -1) {
					bad[v] = true;
					continue;
				}

				assert (depth[p] - depth[v] == 2);
				cnt[res[v]]--;
				depth[v]--;
				cnt[p]++;
				res[v] = p;
				sum--;
			}

			StringBuilder sb = new StringBuilder();
			sb.append("YES\n");
			for (int i = 1; i < n; i++)
				sb.append(res[i] + 1).append(" ");
			System.out.println(sb.toString());
		}
	}

	static class FastReader {

		BufferedReader br;

		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				}
				catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

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

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			}
			catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}
}