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>
#include<algorithm>
using namespace std;
void solve(int n,int k){
    	int b[n+1];
		for(int i=0;i<(n+1);i++)b[i] = 0;
		int count=0;
		vector<int> a;
		for(int i=n;i>0;i--){
			if(i>k){
				count++;
				b[i]=1;
				a.push_back(i);
			}
			else if(i<k && b[i]==0){
				count++;
				b[i]=1;
				a.push_back(i);
				b[k-i]=1;
			}
		}
		cout<<count<<"\n";
		for(int i=0;i<count;i++)
		cout<<a[i]<<" ";
		cout<<"\n";
}
int main(){
	int t;
	cin>>t;
	while(t--){
	    int n,k;cin>>n>>k;
	    solve(n,k);
	}
}