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;
 
int32_t main(){
	ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
	//freopen ("photo.in", "r", stdin);
	//freopen("photo.out", "w", stdout);
	int t;
	cin >> t;
	while (t --){
		int n, m;
		cin >> n >> m;
		vector <int> vc;
		for (int i = 1; i <= n; i ++){
			if (i >= (m + 1) / 2 && i != m){
				vc.push_back(i);
			}
		}
		cout << vc.size() << '\n';
		for (int i = 0; i < int(vc.size()); i ++){
			cout << vc[i] << ' ';
		}
		cout << '\n';
	}
}