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.util.Scanner;


public class P403_A {

    
    static Scanner jin = new Scanner(System.in);    // New scanner object
    
        
    public static void main(String[] args) {
    
        
    int t ;
    
    do{ 
        t= jin.nextInt();       
                         }while( (t<1) ^ (5<t) );
        
    
    int[][] TEST = new int[t][2];
    
        for(int i=0 ; i<t ; i++){
                                TEST[i][0]=jin.nextInt(); // TEST[i][0] stands for n 
                                TEST[i][1]=jin.nextInt(); // TEST[i][1] is p 
                                }
    
        
    for (int i=0 ; i<t ; i++) {
        
    int q = ( 2 * TEST[i][0]) + TEST[i][1] ; 
        
        
    Graph_loop:
        
    for (int a = 1 ; a <=TEST[i][0] ; a++) {
        
        for(int b=(a+1) ; b<=TEST[i][0] ; b++){     
          System.out.println( a +" "+b ); 
          q-- ;
                                            
         if(q==0) break Graph_loop ; 
         // So we don't have more edges && we're done in this oprt ! 
                                              } 
        
    }
    
    
    }// Test circuit 
    
    }// main()

}//class
