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:
import java.util.*;
import java.lang.*;
public class Codeforces {
    static Scanner sr = new Scanner(System.in);
    static int gcd(int a, int b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }
    public static void main(String[] args) throws java.lang.Exception {
        int T=sr.nextInt();
        StringBuffer ans=new StringBuffer();
        while(T-->0)
        {
            int n=sr.nextInt();
            int k=sr.nextInt();
            ArrayList<Integer>a=new ArrayList<>();
            int x=k/2;
            if(k%2!=0)
                x++;
            for(int i=x;i<=n;i++){
                if(i!=k)
                    a.add(i);
            }
            ans.append(a.size()+" "+'\n');
            for(int i=0;i<a.size();i++) {
                ans.append(a.get(i) + " ");
            }
            ans.append('\n');
        }
        System.out.println(ans);

    }
}