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(){
	ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
    //freopen("input.txt","r",stdin);
    //freopen("output.txt","w",stdout);
	int T;
	cin>>T;
	for(int t=0;t<T;t++){
		int n,k;
		cin>>n>>k;
		if(n==1&&k==1){cout<<0<<endl;continue;}
		if(k<=3){
			if(k==2){
				int m=n-1;
				cout<<m<<endl;
				cout<<1<<" ";
				for(int i=3;i<=n;i++)
					cout<<i<<" ";
				cout<<endl;
		}else{
			if(k==1){
				cout<<n-1<<endl;
				for(int i=2;i<=n;i++)
						cout<<i<<" ";
					cout<<endl;
			}
			else{
				cout<<n-2<<endl;
				cout<<1<<" ";
				for(int i=4;i<=n;i++)
						cout<<i<<" ";
					cout<<endl;
				
			}
		}
		}else{
			if(k%2==0){
				int m=n-k/2;
				cout<<m<<endl;
				for(int i=k/2;i<=n;i++)
					if(i!=k)cout<<i<<" ";
				cout<<endl;
			}else{
				int m=n-k/2-1;
				cout<<m<<endl;
				for(int i=k/2+1;i<=n;i++)
					if(i!=k)cout<<i<<" ";
				cout<<endl;
			}
		}
	}
    return 0;
}