Let's call an undirected graph of n vertices p-interesting, if the following conditions fulfill: 

  * the graph contains exactly 2n + p edges; 
  * the graph doesn't contain self-loops and multiple edges; 
  * for any integer k (1 ≤ k ≤ n), any subgraph consisting of k vertices contains at most 2k + p edges. 



A subgraph of a graph is some set of the graph vertices and some set of the graph edges. At that, the set of edges must meet the condition: both ends of each edge from the set must belong to the chosen set of vertices. 

Your task is to find a p-interesting graph consisting of n vertices.

Input

The first line contains a single integer t (1 ≤ t ≤ 5) — the number of tests in the input. Next t lines each contains two space-separated integers: n, p (5 ≤ n ≤ 24; p ≥ 0; <image>) — the number of vertices in the graph and the interest value for the appropriate test. 

It is guaranteed that the required graph exists.

Output

For each of the t tests print 2n + p lines containing the description of the edges of a p-interesting graph: the i-th line must contain two space-separated integers ai, bi (1 ≤ ai, bi ≤ n; ai ≠ bi) — two vertices, connected by an edge in the resulting graph. Consider the graph vertices numbered with integers from 1 to n. 

Print the answers to the tests in the order the tests occur in the input. If there are multiple solutions, you can print any of them.

Examples

Input

1
6 0


Output

1 2
1 3
1 4
1 5
1 6
2 3
2 4
2 5
2 6
3 4
3 5
3 6
//package acc;
import java.util.*;
import java.io.*;
import java.math.BigInteger;
   public  class ACC { 
//************Main*****************//
         
         public static void main(String[] args) throws IOException
			 {
             //   PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));
              //  Scanner in=new Scanner (System.in);
               InputStream inputStream = System.in;
                OutputStream outputStream = System.out;
                InputReader in = new InputReader(inputStream);
                PrintWriter out = new PrintWriter(outputStream);
                
                int t=in.nextInt();
                while(t--!=0){
                    int n=in.nextInt();
                int p=in.nextInt();
                int sum=0;
                boolean ok=false;
                for(int i=1;i<n;i++){
                    for(int j=i+1;j<=n;j++){
                        if(sum==2*n+p){
                            ok=true;
                            break;
                        } 
                        sum++;
                        out.println(i+" "+j);
                    }
                }
                }
                out.close();
         }
         
   }
    class Pair implements Comparable<Pair>{
    int x,y;
    public  Pair(int X,int Y){
        super();
x=X;
y=Y;
}
    @Override
      public int compareTo(Pair p){
          if((x)==(p.x)) return Integer.compare((y), (p.y));
       return Integer.compare((x), (p.x));
}
  }

class InputReader {
    private BufferedReader reader;
    private StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream));
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }
    public long nextLong(){
        return Long.parseLong(next());
    }
}