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.*;

public class A implements Runnable {
	
	private void solve() throws IOException {
		int t = nextInt();
		while (t --> 0) {
			int n = nextInt(), p = nextInt(), need = n * 2 + p;
			for (int dist = 1; dist <= n / 2 && need > 0; dist++)
				for (int v = 0; v < n && need > 0; v++, need--)
					println(v + 1, (v + dist) % n + 1);
		}
	}
	
	public static void main(String[] args) {
		new A().run();
	}
	
	BufferedReader reader;
	StringTokenizer tokenizer;
	PrintWriter writer;
	
	public void run() {
		try {
			String file = "";
			file = "console";
			if (file.equals("console")) {
				reader = new BufferedReader(new InputStreamReader(System.in));
				writer = new PrintWriter(System.out);
			} else if (file.equals("")) {
				reader = new BufferedReader(new FileReader(new File("input.txt")));
				writer = new PrintWriter(new File("output.txt"));
			} else {
				reader = new BufferedReader(new FileReader(new File(file + ".in")));
				writer = new PrintWriter(new File(file + ".out"));
			}
			solve();
			writer.close();
		} catch (Exception e) {
			e.printStackTrace();
			System.exit(261);
		}
	}
	
	void halt() {
		writer.close();
		System.exit(0);
	}
	
	void print(Object... objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0) writer.print(' ');
			writer.print(objects[i]);
		}
	}
	
	void println(Object... objects) {
		print(objects);
		writer.println();
	}
	
	String nextLine() throws IOException {
		return reader.readLine();
	}
	
	String nextToken() throws IOException {
		while (tokenizer == null || !tokenizer.hasMoreTokens())
			tokenizer = new StringTokenizer(nextLine());
		return tokenizer.nextToken();
	}
	
	int nextInt() throws NumberFormatException, IOException {
		return Integer.parseInt(nextToken());
	}
	
	long nextLong() throws NumberFormatException, IOException {
		return Long.parseLong(nextToken());
	}
	
	double nextDouble() throws NumberFormatException, IOException {
		return Double.parseDouble(nextToken());
	}
}