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;
int main(){
    int t;
    cin>>t;
    while(t--){
        int n,k;
        cin>>n>>k;
        //n=7 k=4 cnt=3=n-k 1 2 3 4 5 6 7 choose 6 1 2 3 can add up to 6 but 3 4 5 can't!
        //取数的方向反了 其实是题意理解不透彻 因为是求和所以前面的可以凑在一起可是比较后面的一段就不可以 因为只会越来越大 不能凑数
        //向上取整：(k+1)/2
        cout<<n-(k+1)/2<<endl;
        for(int i=(k+1)/2;i<k;i++){
            cout<<i<<' ';
        }
        for(int i=k+1;i<=n;i++){
            cout<<i<<' ';
        }cout<<endl;
    }
}