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;
#define maxn 2005
#define ll long long
#define mod 1000000007

int n, k;
vector<int> v;

int main()
{
	//ios::sync_with_stdio(false), cin.tie(0);
	//freopen("a_example", "r", stdin);
	//freopen("out1.txt", "w", stdout);
	int T;
	cin >> T;
	while (T--)
	{
		scanf("%d%d", &n, &k);
		v.clear();
		for (int i = (k + 1) / 2; i < k; i++)
			v.push_back(i);
		for (int i = k + 1; i <= n; i++)
			v.push_back(i);
		printf("%d\n", v.size());
		for (int x : v)
			printf("%d ", x);
		printf("\n");
	}

	return 0;
}