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 all(v) v.begin(),v.end()
using namespace std;
void fast()
{
    std::ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
}



int main()
{
    fast();

    int tt; cin >> tt;
    while (tt--)
    {
        int n, k; cin >> n >> k;
        cout << (n - k) + (k / 2) << endl;
        for (int i = k + 1; i <= n; i++)
            cout << i << ' ';
        for (int i = (k + 1) / 2; i < k; i++)
            cout << i << ' ';
        cout << endl;
    }
    
    return 0;
}