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.*;
import java.util.StringTokenizer;

public class Graph {
    FastScanner in;
    PrintWriter out;

    public void solve() throws IOException {
        int t = in.nextInt();
        for (int tc = 0; tc < t; tc++) {
            int n = in.nextInt();
            int p = in.nextInt();

            boolean[][] conn = new boolean[n][n];

            int edges = 0;
            for (int i = 0; i < n; i++) {
                conn[i][(i + 1) % n] = true;
                conn[(i + 1) % n][i] = true;
                edges++;
                conn[i][(i + 2) % n] = true;
                conn[(i + 2) % n][i] = true;
                edges++;
            }

            for (int i = 0; i < n; i++) {
                for (int j = i + 1; j < n; j++) {
                    if (!conn[i][j] && edges < 2 * n + p) {
                        conn[i][j] = true;
                        conn[j][i] = true;
                        edges++;
                    }
                }
            }

            for (int i = 0; i < n; i++) {
                for (int j = i + 1; j < n; j++) {
                    if (conn[i][j]) {
                        out.printf("%d %d\n", i + 1, j + 1);
                    }
                }
            }
        }
    }

    public void run() {
        try {
            in = new FastScanner(System.in);
            out = new PrintWriter(System.out);

            solve();

            out.close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
        }


        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
    }

    public static void main(String[] arg) {
        new Graph().run();
    }
}