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;
import java.io.OutputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.io.InputStream;

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

class TaskC {

    public void solve(int testNumber, Scanner in, PrintWriter out) {

        int test = in.nextInt();

        while ( test > 0) {
            test--;
            int n = in.nextInt();
            int p = in.nextInt();


            boolean G[][] = new boolean[n+1][n+1];
            int edge[] = new int[n+1];
            for (int i = 0; i < 2*n+p; i++) {

                int root = 1, other = 1;
                int min = 1000;
                for (int j = 1; j <= n; j++) {
                    if (min > edge[j]) {
                        min = edge[j];
                        root = j;
                    }
                }


                min = 1000;
                for (int j = 1; j <= n; j++) {
                    if (G[root][j] || root == j)
                        continue;
                    if (min > edge[j]) {
                        min = edge[j];
                        other = j;
                    }
                }

                edge[other]++;
                edge[root]++;
                G[other][root] = G[root][other] = true;
            }

            for (int i = 1; i <= n; i++) {
                for (int j = i+1; j <= n; j++) {

                    if (G[i][j])
                        out.println(i + " " + j);
                }
            }
        }

    }
}

