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.Scanner;

public class Antiknapsack {

	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in); 

		int t = scan.nextInt();
		int k, n;
		
		for (;t > 0; t--) {
			n = scan.nextInt();
			k = scan.nextInt();
			
			int count = (int) (Math.max(0, n - k) + Math.max(k - Math.ceil(k * 1.0 / 2), 0));
			System.out.println(count);
			
			// greater than k till n 
			for(int i = k + 1 ; i <= n; i++) {
				System.out.print(i + " ");
			}  
			
			// smaller than k till half
			for(int i = k - 1; i >= Math.ceil(k * 1.0 / 2); i--) {
				System.out.print(i + " ");
			}
			
			System.out.println();
		}

	}

}