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.awt.Point;
import java.io.*;
import java.util.*;
import java.math.BigInteger;

public class GraphSearch {
    static class Solver {
        MyReader mr = new MyReader();

        public void solve() {
            int t = mr.nextInt();
            while(t-- > 0){
                int n = mr.nextInt();
                int p = mr.nextInt();

//                int[][] g = new int[n][n];

                int k = n+n+p;

                StringBuilder res = new StringBuilder();
                for (int i = 0; i < n && k > 0; i++) {
                    for (int j = i+1; j < n && k > 0; j++) {
                        if(k > 0){
                            res.append(i+1).append(" ").append(j+1).append("\n");
                            k--;
                        }
                    }
                }

                System.out.println(res.toString());
            }
        }
    }

    public static void main(String[] args) {
        new Solver().solve();
    }

    static class MyReader {
        BufferedReader br;
        StringTokenizer st;

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

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    e.printStackTrace();
                }
            }

            return st.nextToken();
        }

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

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

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

        String nextLine() {
            String res = "";
            try {
                res = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }

            return res;
        }

        Integer[] nextIntArray(int n) {
            Integer[] arr = new Integer[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }

            return arr;
        }

        Long[] nextLongArray(int n) {
            Long[] arr = new Long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }

            return arr;
        }

        String[] nextStringArray(int n) {
            String[] arr = new String[n];
            for (int i = 0; i < n; i++) {
                arr[i] = next();
            }
            return arr;
        }
    }

    static void swap(int[] arr, int i, int j) {
        int tmp = arr[i];
        arr[i] = arr[j];
        arr[j] = tmp;
    }

}


