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 Codeforces {

        static char word[];
        
        public static void main(String[] args) throws IOException {
            Reader.init(System.in);
            int t = Reader.nextInt();
            StringBuilder ans = new StringBuilder();
            
            for(int c = 0; c < t; c++){
                int n = Reader.nextInt();
                int p = Reader.nextInt();
                int x = (2*n+p);
                
                for(int i = 1; i < n; i++){
                    for(int j = n; j > i; j--){
                        if(x != 0){
                            ans.append(i).append(' ').append(j).append('\n');
                            x--;
                        }
                    }
                }
            }
            
            System.out.print(ans);
            
        }
     }

    class  Pair implements Comparable<Pair>{

        int val;
        int index;

        Pair(int a, int b){
            val = a;
            index = b;
        }

        @Override
        public int compareTo(Pair t) {
            int a = val - t.val;
            if(a == 0)
                return index - t.index;
            return a;
        }

    }



    class Reader {

        static BufferedReader reader;
        static StringTokenizer tokenizer;

        public static int pars(String x) {
            int num = 0;
            int i = 0;
            if (x.charAt(0) == '-') {
                i = 1;
            }
            for (; i < x.length(); i++) {
                num = num * 10 + (x.charAt(i) - '0');
            }

            if (x.charAt(0) == '-') {
                return -num;
            }

            return num;
        }

        static void init(InputStream input) {
            reader = new BufferedReader(
                    new InputStreamReader(input));
            tokenizer = new StringTokenizer("");
        }

        static void init(FileReader input) {
            reader = new BufferedReader(input);
            tokenizer = new StringTokenizer("");
        }

        static String next() throws IOException {
            while (!tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(
                        reader.readLine());
            }
            return tokenizer.nextToken();
        }

        static int nextInt() throws IOException {
            return pars(next());
        }

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

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