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

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;

public class C {

    
    
    
    static StringBuilder sb=new StringBuilder();
    static void parse(String l, int[] here) {
        sb.setLength(0);
        int len=l.length(), j=0;
        for (int i=0; i<len; i++) {
            char c=l.charAt(i);
            if(c==' ') {
                here[j++]=Integer.parseInt(sb.toString());
                sb.setLength(0);
            } else {
                sb.append(c);
            }
        }
        if(sb.length()>0) {
            here[j++]=Integer.parseInt(sb.toString());
        }
    }
    
    static void run_stream(InputStream ins) throws IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        int t=Integer.parseInt(br.readLine());
        for (int i=0; i<t; i++) {
            String[] s=br.readLine().split(" ");
            int n=Integer.parseInt(s[0]);
            int p=Integer.parseInt(s[1]);
            int cnt=0;
            sb.setLength(0);
            for (int j=1; j<=n&&cnt<2*n+p; j++) {
                for (int k=j+1; k<=n&&cnt<2*n+p; k++) {
                    cnt++;
                    sb.append(j+" "+k+"\n");
                }
            }
            
            System.out.println(sb.toString());
        }
    }

    public static void main(String[] args) throws IOException {
        run_stream(System.in);
    }

}
