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.*;
import java.io.*;

public class Main{

    BufferedReader in;
    StringTokenizer str = null;
    PrintWriter out;

    private String next() throws Exception{
    	if (str == null || !str.hasMoreElements())
    	    str = new StringTokenizer(in.readLine());
    	return str.nextToken();
    }
    
    private int nextInt() throws Exception{
	   return Integer.parseInt(next());
    }
    
    public void run() throws Exception{
    	in = new BufferedReader(new InputStreamReader(System.in));
    	out = new PrintWriter(System.out);

        int t = nextInt();
        for(int i=0;i<t;i++)
            solve();

        out.close();	
    }

    private void solve() throws Exception{
        int n = nextInt(), p = nextInt();
        boolean g[][] = new boolean[n][n];
        int deg[] = new int[n];
        int c = 0;

        while(c < 2 * n + p) {
            int f = 0;
            for(int i=1;i<n;i++){
                if (deg[i] < deg[f]) {
                    f = i;
                }
            }

            int s = -1;
            for(int i=0;i<n;i++){
                if (i == f) continue;
                if (g[f][i]) continue;
                if (s == -1 || deg[i] < deg[s]) {
                    s = i;
                }
            }
            // System.out.println(f + " " +s);
            g[f][s] = g[s][f] = true;
            deg[s]++;
            deg[f]++;
            c++;
        }

        // System.out.println(Arrays.toString(deg));

        for(int i=0;i<n;i++){
            for(int j=i+1;j<n;j++){
                if (g[i][j]) {
                    out.println((i+1) + " " + (j+1));
                }
            }
        }
    }

    public static void main(String args[]) throws Exception{
	   new Main().run();
    }
}