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.*;

public class Main {
    
    public static void main(String[] args) throws Exception {
        FastScanner scan = new FastScanner(System.in);
        int t = scan.nextInt();
        for (int index = 0; index < t; ++index) {
            int n = scan.nextInt();
            int p = scan.nextInt();
            int left = 2 * n + p;
            StringBuilder builder = new StringBuilder(left * 10);
            boolean[][] connected = new boolean[n][n];
            for (int step = 1; left > 0; ++step) {
                for (int j = 0; j < step; ++j) {
                    int from = j;
                    while (left > 0) {
                        int to = (from + step) % n;
                        if (connected[from][to]) {
                            break;
                        }
                        connected[from][to] = connected[to][from] = true;
                        --left;
                        builder.append(String.format("%d %d\n", from + 1, to + 1));
                        from = to;
                    }
                }
            }
            System.out.print(builder.toString());
            System.out.flush();
        }
    }
}

class FastScanner {
    BufferedReader in;
    StringTokenizer tok;

    public FastScanner(InputStream in) {
        this.in = new BufferedReader(new InputStreamReader(in));
        tok = new StringTokenizer("");
    }

    private String tryReadNextLine() {
        try {
            return in.readLine();
        } catch (Exception e) {
            throw new InputMismatchException();
        }
    }

    public String nextToken() {
        while (!tok.hasMoreTokens()) {
            tok = new StringTokenizer(next());
        }
        return tok.nextToken();
    }

    public String next() {
        String newLine = tryReadNextLine();
        if (newLine == null)
            throw new InputMismatchException();
        return newLine;
    }

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

    public long nextLong() {
        return Long.parseLong(nextToken());
    }

}