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.Scanner;
import java.math.BigDecimal;
import java.util.Arrays;
import java.util.*;
import java.io.*;
public class Main {
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		long t=sc.nextLong();
		while(t--!=0) {
			long n=sc.nextLong();
			long k=sc.nextLong();
			long x=k/2;
			long sum=0;
			for(long i=k+1;i<=n;i++) {
				sum++;
			}
			sum+=x;
			System.out.println(sum);
			for(long i=k-1,j=0;j<x;j++,i--) {
				System.out.print(i+" ");
			}
			for(long i=k+1;i<=n;i++) {
				sum++;
				System.out.print(i+" ");
			}
			System.out.print("\n");
	}
}
}