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
#define mod 1000000007
#define inf 0x3f3f3f3f
int main(){
    ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
    std::cout << std::fixed << std::setprecision(0);
    int testCases ;
    cin >> testCases ;
    while(testCases--){
        ll n, k ;
        cin >> n >> k ;
        ll ans=0 ;
        vector<ll> val ;
        ans+= n-(k+1)/2 ;
        for(ll i=(k+1)/2; i<=n ;i++){
            if(i==k)
                continue ;
            val.push_back(i) ;
        }
        // ll sum = 0 ;
        // for(ll i=1 ; i<k ; i++){
        //     if(sum+i<k){
        //         ans++ ;
        //         val.push_back(i);
        //         sum+=i ;
        //     }else{
        //         break ;
        //     }
        // }
        cout <<ans<<endl ;
        for(ll i=0 ;i<val.size() ;i++){
            cout << val[i] <<" " ;
        }
        cout << endl ;
    }
    return 0 ;
}