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;
        if(k%2==0){
        	cout<<n-k+k/2<<"\n";
        	for(int i=k/2;i<k;i++){
        		cout<<i<<" ";
        	}
        	for(int i=k+1;i<=n;i++){
        		cout<<i<<" ";
        	}
        }
        else{
        	cout<<n-k+k/2<<"\n";
        	for(int i=2;i<k;i=i+2){
        		cout<<i<<" ";
        	}
        	for(int i=k+1;i<=n;i++){
        		cout<<i<<" ";
        	}
        }
        cout<<"\n";
    }
}