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;

void solve() {
	int n, k;
	cin >> n >> k;

	vector<int> ans;
	for(int i = k + 1; i <= n; ++i)
		ans.push_back(i);

	for(int i = (k + 1) / 2; i < k; ++i)
		ans.push_back(i);

	sort(ans.begin(), ans.end());

	cout << ans.size() << "\n";
	for(auto x: ans)
		cout << x << " ";
	cout << "\n";
}

int main() {
	int t;
	cin >> t;

	while(t--)
		solve();
}