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 rep(i,n) for(ll i=0;i<n;i++)
#define rev(i,n) for(ll i=n-1;i>=0;i--)


int main() 
{ 
    ll t;
    cin >> t;
    while(t--)
    {
        ll n,k;
        cin>>n>>k;
        ll ans = n-k;
        if(k%2)
        ans+=(k-1)/2;
        else 
        ans+=k/2;
        cout<<ans<<endl;
        ll i;
        if(k%2)
        i=(k/2)+1;
        else 
        i=k/2;
        for(i;i<k;i++)
        {
            cout<<i<<" ";
        }
        for(ll i=k+1;i<=n;i++)
        if(i!=n)
        cout<<i<<" ";
        else 
        cout<<i;
        cout<<endl;
    } 
}