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.ArrayList;
import java.util.List;
import java.util.Scanner;
import java.util.stream.Collectors;
public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int t = in.nextInt();
        while (t-- != 0) {
            int n = in.nextInt();
            int k = in.nextInt();
            int[] vis = new int[1000 + 1];
            vis[k] = 1;
            for (int i = 1; i <= (k - 1)/2; i++) {
                vis[i] = 1;
            }
            int ans = 0;
            int[] result = new int[n];
            for (int i = 1; i <= n; i++) {
                if (vis[i] == 0) {
                    result[ans++] = i;
                }
            }
            if (ans == 0) {
                System.out.println(0);
            } else {
                System.out.println(ans);
                for (int i = 0; i < ans; i++) {
                    if (i != ans - 1) {
                        System.out.print(result[i] + " ");
                    } else {
                        System.out.println(result[i]);
                    }
                }
            }
        }
        in.close();
    }
}