Problem: You are given two integers n and k. You are asked to choose maximum number of distinct integers from 1 to n so that there is no subset of chosen numbers with sum equal to k.

A subset of a set is a set that can be obtained from initial one by removing some (possibly all or none) elements of it.

Input

The first line contains the number of test cases T (1 ≤ T ≤ 100).

Each of the next T lines contains two integers n and k (1 ≤ k ≤ n ≤ 1000) — the description of test cases.

Output

For each test case output two lines. In the first line output a single integer m — the number of chosen integers.

In the second line output m distinct integers from 1 to n — the chosen numbers.

If there are multiple answers, print any. You can print the numbers in any order.

Example

Input


3
3 2
5 3
1 1


Output


2
3 1 
3
4 5 2 
0

Solution (in JAVA):

Solution:
//This code is written by प्रविण शंखपाळ 


import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Collections;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.LinkedList;
import java.util.Stack;
import java.util.Queue;
import java.util.PriorityQueue;
import java.util.List;
import java.util.HashSet;
import java.util.LinkedHashSet;
import java.util.TreeSet;
import java.util.Map;
import java.util.HashMap;
import java.util.Scanner;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.Vector;
import javafx.util.Pair;

public class Ginny_Weasley {

	public static void main(String[] args) {
		try {
			FastReader fr = new FastReader();

			int T = fr.nextInt();

			while (T > 0) {

				int n = fr.nextInt();

				int k = fr.nextInt();

				System.out.println();

				System.out.println(k / 2 + n - k);

				for (int i = (k + 1) / 2; i < k; i += 1) {

					System.out.print(i + " ");
				}

				for (int i = k + 1; i <= n; i += 1) {

					System.out.print(i + " ");
				}

				T--;
			}

		} catch (Exception e) {
			return;
		}

	}

	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;
		}
	}
}