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.OutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		FastScanner in = new FastScanner(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskA solver = new TaskA();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskA {
        public void solve(int testNumber, FastScanner in, PrintWriter out) {
                int t = in.nextInt();
                for (int test = 0; test < t; test++) {
                        int n = in.nextInt();
                        int p = in.nextInt();
                        boolean[][] edge = new boolean[n][n];
                        for (int i = 0; i < n; i++)
                                edge[i][(i + 1) % n] = edge[(i + 1) % n][i] = true;
                        for (int i = 0; i < n; i++)
                                edge[i][(i + 2) % n] = edge[(i + 2) % n][i] = true;
                        for (int i = 0; i < n; i++)
                                for (int j = 0; j < n; j++) {
                                        if (i == j || p == 0 || edge[i][j])
                                                continue;
                                        edge[i][j] = edge[j][i] = true;
                                        p--;
                                }
                        for (int i = 0; i < n; i++)
                                for (int j = i + 1; j < n; j++)
                                        if (edge[i][j])
                                                out.println((i + 1) + " " + (j + 1));
                }
        }
}

class FastScanner {
        BufferedReader reader;
        StringTokenizer tokenizer;

        public FastScanner(InputStream inputStream)  {
                reader = new BufferedReader(new InputStreamReader(inputStream));
        }

        public String nextToken() {
                while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                        String line;
                        try {
                                line = reader.readLine();
                        } catch (IOException e) {
                                return null;
                        }
                        tokenizer = new StringTokenizer(line);
                }
                return tokenizer.nextToken();
        }

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

        }

