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.BufferedInputStream;
import java.util.*;

public class DemoApplication {
    static class Node{
        int id;
        int ac, noac;
        double prob;
        Node(){
            id = ac = noac = 0;
            prob = 0.0;
        }
    }
    static class cmp implements Comparator<Node>{
        public int compare(Node a, Node b){
            return (int)(a.prob - b.prob);
        }
    }
    public static void main(String[] args) {
Scanner sc = new Scanner(new BufferedInputStream(System.in));
        int t = sc.nextInt();
        while(t-->0){
            int n = sc.nextInt();
            int p = sc.nextInt();
            int cnt = 0;
            for(int i = 1; i <= n; i++){
                int flag = 0;
                for(int j = i+1; j <= n; j++){
                    System.out.println(i +" "+ j);
                    cnt++;
                    if(cnt==2*n+p) {
                        flag = 1;
                        break;
                    }
                }
                if(flag==1)break;
            }
        }
    }
}

	   			      	  	 				  		   		