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 fo(i,a,b) for(int i = a; i <= b; i ++)
using namespace std;

int res,n,k,t;
int main()
{
    ios_base::sync_with_stdio(false),cin.tie(NULL),cout.tie(NULL);
    cin >> t;
    fo(pp,1,t)
    {
        res = 0;
        cin >> n >> k;
        if(n > k) res += n - k;
        res += k / 2;
        cout << res <<"\n";
        if(n > k)
            fo(i,k + 1,n) cout << i<<" ";
        for(int i = k - 1 ; i >= k - k / 2; i --)
            cout <<i<<" ";
        cout<<"\n";

    }
}