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 <iostream>

using namespace std;

int main() {
	cin.tie(0);cin.sync_with_stdio(0);cout.tie(0);
	int t; cin  >> t; while (t--) {
		
		int n,k;
		
		
	cin  >> n >> k;
	cout << n-k + k/2 <<  endl;
	for (int i=(k+1)/2;i< k;i++) cout << i << " ";
	for (int i=k+1;i<= n;i++) cout << i << " ";
	cout << endl;
	}
	return 0;
}