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 int long long
#define double long double
#define F first
#define S second
#define pb push_back
#define lg2(x) 31-__builtin_clz(x)
#define lg(x,b) log(b)/log(x)

int t,n,k,a,ans;

int32_t main(){
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);

cin>>t;
while(t--){
    cin>>n>>k;
    ans=n-k;
    ans+=k/2;
    if(k%2)a=k/2+1;
    else a=k/2;
    cout<<ans<<"\n";
    for(int i=a;i<k;i++)cout<<i<<" ";
    for(int i=k+1;i<=n;i++)cout<<i<<" ";
    cout<<"\n";
}

return 0;
}