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 matrix;

import java.util.*;

public class CodeFOR 
{
	public static void main(String[] args)
	{
		Scanner sc=new Scanner(System.in);
		int T=sc.nextInt();
		while(T-->0)
		{
			int n=sc.nextInt(),k=sc.nextInt(),i;
			int start=k%2==0?k/2:k/2+1;
			System.out.println((n-k)+(k-start));
			
			for(i=start;i<k;i++)
				System.out.print(i+" ");
			for(i=k+1;i<=n;i++)
				System.out.print(i+" ");
			System.out.println();
		}
	}
}