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;
		int ans=0;
		for(int i=k+1;i<=n;i++){
			ans++;
		}
		for(int i=(k+1)/2;i<k;i++){
			ans++;
		}
		cout<<ans<<endl;
		for(int i=k+1;i<=n;i++){
			cout<<i<<" ";
		}
		for(int i=(k+1)/2;i<k;i++){
			cout<<i<<" ";
		}
		cout<<endl;
	}
}
//3-----3, 1 2, 
// 1 2 3 4 5

// 5-----5 , 1 4 ,2 3
// 7-----7 , 1 6 ,2 5 ,3 4
// 1 2 3  4 5 6 7 8
// 6-----6 , 1 5 ,2 4 ,3 3
// 1 2 3  4 5  6 7 8


// 2-----2
// 1 2 3