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 B{
   public static void main(String ars[]){
        //BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        Scanner in = new Scanner(System.in);
        int t = in.nextInt();
        while(t-->0){
            int n = in.nextInt();
            int p = in.nextInt();
            ArrayList<ArrayList<Integer>> graph = new ArrayList<>();
            for(int i=0;i<n;i++){
                graph.add(new ArrayList<Integer>());
            }
            int edges=0;
            int current=0;
            int jump =1;
            while(edges < 2*n+p){
                if(jump==n)
                    break;
                graph.get(current).add((current+jump));
                current = current+1;
                if(current==n || current+jump>=n){
                    current = 0;
                    jump++;
                }
                edges++;
            }
            for(int i=0;i<n;i++){
                ArrayList<Integer> temp = graph.get(i);
                for(int j=0;j<temp.size();j++){
                    System.out.println((i+1)+" "+(temp.get(j)+1));
                }
            }
        }
        in.close();
   }
}