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.Scanner;

public class SearchingForGraph {
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int T = scan.nextInt();
		for (int test = 0; test < T; test++) {
			int N = scan.nextInt();
			int P = scan.nextInt();
			int dead = 2 * N + P;
			StringBuilder sb = new StringBuilder();
			int Z = 0;
			for (int i = 0; i < N; i++) {
				for (int j = i + 1; j < N; j++) {
					sb.append(i + 1 + " " + (j + 1) + "\n");
					Z++;
					if (Z == dead) {
						i = N + 1;
						j = N + 1;
					}
				}
			}
			System.out.println(sb);
		}
		scan.close();
	}
}
