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.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Solver {

	public static void main(String[] Args) throws NumberFormatException,
			IOException {
		new Solver().Run();
	}

	PrintWriter pw;
	StringTokenizer Stok;
	BufferedReader br;

	public String nextToken() throws IOException {
		while (Stok == null || !Stok.hasMoreTokens()) {
			Stok = new StringTokenizer(br.readLine());
		}
		return Stok.nextToken();
	}

	public int nextInt() throws NumberFormatException, IOException {
		return Integer.parseInt(nextToken());
	}

	public double nextDouble() throws NumberFormatException, IOException {
		return Double.parseDouble(nextToken());
	}

	public long nextLong() throws NumberFormatException, IOException {
		return Long.parseLong(nextToken());
	}

	int kolVert, kolAdd;
	
	public void Run() throws NumberFormatException, IOException {
		//br = new BufferedReader(new FileReader("input.txt")); pw = new PrintWriter("output.txt");
		br=new BufferedReader(new InputStreamReader(System.in));  pw=new PrintWriter(new OutputStreamWriter(System.out));
		
		int kolTest=nextInt();
		for (int z=0; z<kolTest; z++){
			kolVert=nextInt();
			kolAdd=nextInt();
			int kolPrinted=0;
			int toPrint=2*kolVert+kolAdd;
			for (int i=1; i<=kolVert && kolPrinted<toPrint; i++){
				for (int j=i+1; j<=kolVert && kolPrinted<toPrint; j++, kolPrinted++){
					pw.print(i);
					pw.print(' ');
					pw.println(j);
				}
			}
		}
		pw.flush();
		pw.close();
	}

}
