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>
#define mis(x) cout << #x <<" = " <<x<<endl
#define rep(i, a, b) for(int i=(a);(i)<(b);(i)++)
#define re(i,a) rep((i),0,(a))
#define eb emplace_back
#define x first
#define y second
	//	#define cin fin
using namespace std;
typedef long long ll;
ifstream fin("Sisend.txt");
ll t,n,k;
int main(){
	ios::sync_with_stdio(0);cin.tie(0);	cout.tie(0);cerr.tie(0);
	cin>>t;while(t--){
		cin>>n>>k;
		ll vas=0;
		if(n>k)vas+=n-k;
		vas+=k/2;
		cout<<vas<<endl;
		if(k<n)for(int i=k+1;i<=n;i++)cout<<i<<" ";
		for(int i=k/2+k%2;i<k;i++)cout<<i<<" ";
		cout<<endl;
	}
}