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.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;

public class A {
	public static void main(String[] args) {
		try {
			BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
			int tc = 0;
			while (true) {
				String line = br.readLine();
				if (line == null) break;
				System.err.println("--------------TEST CASE " + ++tc + "---------------");
				System.err.println("INPUT");
				System.err.println(line);

				int t = Integer.parseInt(line);

				for (int i = 0; i < t; i++) {
					line = br.readLine();
					System.err.println(line);
					String[] s = line.split(" ");
					int n = Integer.parseInt(s[0]);
					int p = Integer.parseInt(s[1]);
					System.out.println(new A().solve(n, p));
				}
			}
		} catch (IOException io) {
			io.printStackTrace();
		}
	}

	private String solve(int n, int p) {
		List<int[]> l = new ArrayList<int[]>();
		boolean[][] conn = new boolean[n+1][n+1];
		int[] count = new int[n+1];
		while(l.size()<2*n+p) {
			int min = 10100101;
			int idx1 = -1;
			int idx2 = -1;
			for (int i = 1; i <= n; i++) {
				for (int j = i+1; j <= n; j++) {
					if (conn[i][j]) continue;
					int curr = n*n*Math.max(count[i],count[j])+Math.min(count[i],count[j]);
					if (curr<min) {
						min = curr;
						idx1=i;
						idx2=j;
						
					}
				}
			}
			conn[idx1][idx2] = true;
			l.add(new int[]{idx1,idx2});
			count[idx1]++;
			count[idx2]++;
		}
		System.err.println(l.size()+":"+(2*n+p));
		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < l.size(); i++) {
			int[] v = l.get(i);
			sb.append(v[0]).append(" ").append(v[1]).append("\n");
		}
		return sb.toString();
	}
}
