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>
#define ll long long
#define pb push_back
using namespace std;
int main()
{
    ll t;
    cin>>t;
    while(t--){
        ll n,k;

        cin>>n>>k;

        vector<ll>arr,check(n+1,0);
        ll cnt=0;
        for(ll i=k+1;i<=n;i++){
            arr.pb(i);
            cnt++;
        }
        for(int i=k-1;i>=1;i--){
            if(check[i]==0){
                arr.pb(i);
                cnt++;
                check[k-i]=1;
            }
        }
        cout<<cnt<<endl;
        for(int i=0;i<cnt;i++){
            cout<<arr[i]<<" \n"[i==cnt-1];
        }


    }


    return 0;
}