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:
//package codeforces;
import java.util.*;
public class codeforces {
	public static void main(String[] args) {
		//System.out.println(2&4);
		Scanner s=new Scanner(System.in);
		//System.out.println(Math.cbrt(703657519796));
		int t=s.nextInt();
		for(int tt=0;tt<t;tt++) {
			int n=s.nextInt(),k=s.nextInt();
			HashSet<Integer> a=new HashSet<>();
			long ans=0;
			if(k%2==0) {
				ans=n-k/2;
				System.out.println(ans);
				for(int i=k/2;i<=n;i++) {
					if(i!=k) {
						System.out.print(i+" ");
					}
				}
			}else {
				ans=n-k/2-1;
				System.out.println(ans);
				for(int i=k/2+1;i<=n;i++) {
					if(i!=k) {
						System.out.print(i+" ");
					}
				}
				
			}
			System.out.println();
		}
		s.close();
	}
	
	static void sort(int[] a) {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}
}