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.*;
import java.util.*;
public class Main { 
    public static void main(String args[]) {
        Scanner input=new Scanner(System.in);
        int test=input.nextInt();
        for(int t=0;t<test;t++) {
            int n=input.nextInt();
            int p=input.nextInt();
            int count=2*n+p;
            Set<Integer> hash_set[]=new HashSet[n+1];
            for(int i=1;i<=n;i++) {
                hash_set[i]=new HashSet<>();
                hash_set[i].add(i);
            }
            StringBuilder ans=new StringBuilder("");
            for(int i=1;i<n;i++) {
                count--;
                hash_set[i].add(i+1);
                hash_set[i+1].add(i);
                ans.append(i+" "+(i+1)+"\n");
            }
            if(!hash_set[1].contains(n)) {
                count--;
                hash_set[1].add(n);
                hash_set[n].add(1);
                ans.append(1+" "+n+"\n");
            }
            for(int i=1;i<=n;i++) {
                for(int j=1;j<=n;j++) {
                    if(hash_set[i].contains(j)) {
                        continue;
                    }
                    ans.append(i+" "+j+"\n");
                    hash_set[i].add(j);
                    hash_set[j].add(i);
                    count--;
                    if(count==0) {
                        break;
                    }
                }
                if(count==0) {
                    break;
                }
            }
            System.out.println(ans);
        }
    }
}
