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 static java.lang.Math.*;
import static java.util.Arrays.*;

public class Main {

	BufferedReader in;
	PrintWriter out;
	StringTokenizer st = new StringTokenizer("");

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

	void run() throws IOException {
		// in = new BufferedReader(new FileReader("input.txt"));
		// out = new PrintWriter("output.txt");

		if (new File("input.txt").exists())
			in = new BufferedReader(new FileReader("input.txt"));
		else
			in = new BufferedReader(new InputStreamReader(System.in));
		if (new File("output.txt").exists())
			out = new PrintWriter("output.txt");
		else
			out = new PrintWriter(System.out);

		solve();

		in.close();
		out.close();
	}

	void solve() throws IOException {
		int countTest = nextInt();
		for (int test = 0; test < countTest; test++) {
			int n = nextInt();
			int p = nextInt();
			int count = 0;
			for (int i = 0; i < n && count < 2 * n + p; i++)
				for (int j = i + 1; j < n && count < 2 * n + p; j++) {
					count++;
					out.println((i + 1) + " " + (j + 1));
				}
			for (int i = 0; i < n && count < 2 * n + p; i++)
				for (int j = 0; j < i && count < 2 * n + p; j++) {
					count++;
					out.println((i + 1) + " " + (j + 1));
				}
		}
	}

	String nextToken() throws IOException {
		while (!st.hasMoreTokens())
			st = new StringTokenizer(in.readLine());
		return st.nextToken();
	}

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

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

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

	String nextLine() throws IOException {
		st = new StringTokenizer("");
		return in.readLine();
	}

}
