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
#include<bits/stdc++.h>
#define pb push_back
#define fon(i,a,b) for(int i=a;i<b;i++)
using namespace std;
int main(){
	int t;
	cin>>t;
	while(t--){
		int n,k;
		cin>>n>>k;
		vector<int>x;
		int m=0;
		int i=n;
		while(i>k){
			x.pb(i);
			i--;
			m++;
		}
		if(k%2==0){
			fon(j,k/2,k){
				x.pb(j);
				m++;
			}
		}
		else{
			fon(j,(k+1)/2,k){
				x.pb(j);
				m++;
			}
		}
		cout<<m<<endl;
		fon(j,0,m){
			cout<<x[j]<<" ";
		}
		cout<<endl;
		
		
	}
}