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
import java.math.BigDecimal;
import java.math.RoundingMode;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Scanner;
import java.util.Vector;

public class M {

	public static void main(String[] args) {
		Scanner ob = new Scanner(System.in);
		int a1 = ob.nextInt();
		for(int i=0;i<a1;i++)
		{
		int n=ob.nextInt();
		int k=ob.nextInt();
		
		
		for(int j=1;j<=k/2;j++){System.out.print(j+" ");}
		for(int j=k+1;j<=n;j++){System.out.print(j+" ");}
		}		
		/*double a=ob.nextDouble();
		double b=ob.nextDouble();
		BigDecimal c = BigDecimal.valueOf(a);
		BigDecimal d = BigDecimal.valueOf(b);
		System.out.println(c.multiply(d).setScale(0, RoundingMode.DOWN));*/
	}
}