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() {
	ios::sync_with_stdio(0);
	cin.tie(0);

	int t;
	cin >> t;
	while(t--) {
		int n, k;
		cin >> n >> k;
		vector<int> a;
		for(int i=n; i>k; i--) a.push_back(i);
		for(int i=k-1; i>=(k+1)/2; i--) {
			a.push_back(i);
		}
		cout << a.size() << '\n';
		for(int x : a) cout << x << ' ';
		cout << '\n';
	}
}