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.*;
import java.awt.*;

public class Main {
	static BufferedReader br = new BufferedReader( new InputStreamReader(System.in) );
	static StringTokenizer st = new StringTokenizer("");
	static String next()	throws Exception	{
		
		while	( !st.hasMoreTokens() )	{
			String s = br.readLine();
			if	( s == null )	return	null;
			st = new StringTokenizer( s );
		}
		return	st.nextToken();
	}
	
	public static void main(String [] asda)	throws Exception	{
		PrintWriter out = new PrintWriter( new BufferedOutputStream(System.out) );
		//

		int CASES = Integer.parseInt( next() );
		while	(CASES-- > 0)	{
		
		int N = Integer.parseInt( next() );
		int P = Integer.parseInt( next() );
		int edges = (2*N) + P;
		
		ArrayList<Integer> g [] = new ArrayList[N];
		for (int i = 0; i < N; i++)
			g[i] = new ArrayList<Integer>();
		
		for (int i = 0; i < N && edges > 0; i++)	{
			for (int k = i + 1; k < N && edges > 0; k++)	{
				g[i].add(k);
				edges--;
			}
		}

		for (int i = 0; i < N; i++)	{
			for (int v : g[i])
				out.println( (i + 1) + " " + (v + 1) );
		}
		
		}
		//
		out.flush();
		System.exit(0);
	}

}





