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 main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    int T,n,k;
    cin>>T;
    for(int i=0; i<T;i++)
    {
       cin>>n>>k;
       if(k%2==0)
       {
        cout<<((k/2)+(n-k))<<"\n";
       for (int j=(k/2);j<=n;j++)
       {
          if (j!=k) 
            cout<<j<<" ";
       }
       }
       else
       {
        cout<<((k/2)+(n-k))<<"\n";
       for (int j=((k/2)+1);j<=n;j++)
       {
          if (j!=k)  
            cout<<j<<" ";
       }  
       }
       
    }
}