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 pb push_back
#define speed ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0)
using namespace std;
typedef long long ll;
typedef long double ld;
typedef vector <ll> vll;
typedef pair<ll,ll> pll;
typedef vector <pair<ll,ll>> vpll;
typedef vector <vll> vvll;

const ll N=1e5+1;
ll t,n,k;

int main()
{
    speed;
    cin>>t;
    while(t--)
    {
        cin>>n>>k;
        vll ans;
        cout<<n-(k+1)/2<<"\n";
        for(int i=(k+1)/2;i<=n;i++)
            if(i!=k)
                cout<<i<<" ";
        cout<<"\n";
    }
    return 0;
}