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.util.*;
import java.io.*;

public class CodeForces {

	static int[][] G;
	static StringBuilder sol;
	static long totalDist;

	public static void main(String[] args) throws Exception{
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		int num_tests = Integer.parseInt(in.readLine());
		for (int i = 0; i < num_tests; i++) {
			StringTokenizer st = new StringTokenizer(in.readLine(), " ");
			int N = Integer.parseInt(st.nextToken());
			int P = Integer.parseInt(st.nextToken());
			int edges = 2 * N + P;
			for (int ind = 1; ind < N && edges > 0; ind++) {
				for (int j = ind + 1; j <= N && edges > 0; j++) {
					System.out.println(ind + " " + j);
					edges--;
				}
			}
		}
		//PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		//out.close();
	}
}