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
//Author: net12k44
import java.io.*;
import java.util.*;
//public
class Main{//}
    

private void solve() {
	int test = in.nextInt();
	while (test-- > 0){
		int n = in.nextInt() , m = in.nextInt();
		m += n*2;
		for(int i = 1; i <= n; ++i)
		for(int j = i+1; j <= n; ++j){
			if (m == 0) break;
			out.println(i+" "+j);
			m--;
		}
	}
}
    
public static void main (String[] args) throws java.lang.Exception {        
    long startTime = System.currentTimeMillis();

    out = new PrintWriter(System.out);
    new Main().solve();    
    //out.println((String.format("%.2f",(double)(System.currentTimeMillis()-startTime)/1000)));
    out.close();
}

static PrintWriter out;    
static class in {
    static BufferedReader reader = new BufferedReader( new InputStreamReader(System.in) ) ;
    static StringTokenizer tokenizer = new StringTokenizer("");             
    static String next() {      
        while ( !tokenizer.hasMoreTokens() )
            try { tokenizer = new StringTokenizer( reader.readLine() ); }
            catch (IOException e){
                throw new RuntimeException(e);          
            }       
        return tokenizer.nextToken();
    }
    static int nextInt() { return Integer.parseInt( next() ); }     
    static long nextLong(){ return Long.parseLong( next() ); }
}
//////////////////////////////////////////////////
}//
