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;
const int N=1e6+5;
typedef long long ll;
int main()
{
      int t;
      cin>>t;
      while(t--)
      {
            ll n,k;
            cin>>n>>k;
            if(n==1)
            cout<<"0\n";
            else
            {
                ll start=k/2+(k%2);
                cout<<n-start<<"\n";
                for(;start<=n;start++)
                {
                    if(start!=k)
                    cout<<start<<" ";
                }
                cout<<"\n";
            }
      }
}