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 CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;

int t;
int n,k;
int vis[1005];

int main()
{
    scanf ("%d", &t);
    while (t--)
    {
        scanf("%d %d", &n, &k);
        memset(vis, 0, sizeof vis);
        int ans= n-k + k/2;
        printf("%d\n", ans);
        for (int i=n;i>0;i--)
        {
            if (i>k)
            {
                printf("%d%c", i, ans==1?'\n':' ');
                ans--;
            }
            else if (i==k)
                continue;
            else
            {
                if (!vis[i])
                {
                    printf("%d%c", i, ans==1?'\n':' ');
                    vis[k-i]=1;
                    ans--;
                }
                else continue;
            }

        }

    }

    return 0;
}