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 TaskC {
    private FastScanner in;
    private PrintWriter out;

    public void solve() throws IOException {
        int t = in.nextInt();
        for (int test = 0; test < t; test++) {
            int n = in.nextInt(), p = in.nextInt();
            boolean[][] haveEdge = new boolean[n][n];
            int rem = 2 * n + p;

            for (int i = 1; i <= n / 2; i++) {
                for  (int j = 0; j < n; j++) {
                    int to = (j + i) % n;
                    if (to != j && !haveEdge[j][to] && rem > 0) {
                        haveEdge[j][to] = haveEdge[to][j] = true;
                        rem--;
                    }
                }
            }
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    if (haveEdge[i][j] && i < j) {
                        out.println((i + 1) + " " + (j + 1));
                    }
                }
            }
        }

    }

    public void run() {
        try {
            in = new FastScanner();
            out = new PrintWriter(System.out);
            solve();
            out.close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    private class FastScanner {
        private BufferedReader br;
        private StringTokenizer st;

        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

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

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

        public double nextDouble() {
            return Double.parseDouble(next());
        }

    }

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