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;
#define ll long long

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    ll i, j,  n, m, l, t, k, key, res, need; char cch;
    cin>>t;
    while(t--){
            cin>>n>>k;
            l = (k+1)/2;
            cout<<n-l<<endl;
            for(i=l; i<=n; i++)
                if(i!=k) cout<<i<<' ';
            cout<<endl;
    }
    return 0;
}