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.*;
import java.math.*;


public class Main {
    static BufferedReader in;
    static PrintWriter out;
    static StringTokenizer tok;
    

    static void solve() throws Exception {
        int t = nextInt();
        for (int tt = 0; tt < t; tt++) {
            int n = nextInt();
            int p = nextInt();
            Node[] a = new Node[n];
            for (int i = 0; i < n; i++) {
                a[i] = new Node(i+1, 0);
            }
            boolean[][] used = new boolean[n+1][n+1];
            for (int i = 0; i < 2*n + p; i++) {
                for (int j = 1; j < n; j++) {
                    if (!used[a[0].i][a[j].i]) {
                        out.println(a[0].i + " " + a[j].i);
                        a[0].cnt++;
                        a[j].cnt++;
                        used[a[0].i][a[j].i] = true;
                        used[a[j].i][a[0].i] = true;
                        break;
                    }
                }
                Arrays.sort(a);
            }
        }       
    }
    
    static class Node implements Comparable<Node>{
        int i, cnt;
        
        Node(int i, int cnt) {
            this.i = i;
            this.cnt = cnt;
        }
    
        public int compareTo(Node other) {
            return Integer.compare(this.cnt, other.cnt);
        }
    }

    static int sqr(int x) {
        return x*x;
    }
    
    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    static BigInteger nextBigInteger() throws IOException {
        return new BigInteger(next());
    }
    
    static String next() throws IOException {
        while (tok == null || !tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }
    
    static String nextLine() throws IOException {
        tok = new StringTokenizer("");
        return in.readLine();
    }

    static boolean hasNext() throws IOException {
        while (tok == null || !tok.hasMoreTokens()) {
            String s = in.readLine();
            if (s == null) {
                return false;
            }
            tok = new StringTokenizer(s);
        }
        return true;
    }

    public static void main(String args[]) {
        try {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(new OutputStreamWriter(System.out));
            //in = new BufferedReader(new FileReader("input.in"));
            //out = new PrintWriter(new FileWriter("output.out"));
            solve();
            in.close();
            out.close();
        } catch (Throwable e) {
            e.printStackTrace();
            java.lang.System.exit(1);
        }
    }
}