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 CF236_D2_C {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int t = scanner.nextInt();
        for (int i = 0; i < t; i++) {
            solve(scanner);
        }
    }

    private static void solve(Scanner scanner) {
        int n = scanner.nextInt();
        int p = scanner.nextInt();
        StringBuilder out = new StringBuilder();
        int count = 2 * n + p;
        for (int i = 1; i <= n; i++) {
            for (int j = i + 1; j <= n; j++) {
                out.append(i).append(" ").append(j).append("\n");
                count--;
                if (count == 0) {
                    System.out.print(out);
                    return;
                }

            }
        }
//        for (int i = 1; i <= p; i++) {
//            for (int j = i + 1; j <= n; j++) {
//                out.append(j).append(" ").append(i).append("\n");
//            }
//        }
    }
}
