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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Solution {

    private final static FastReader in = new FastReader();
    private static final PrintWriter out = new PrintWriter(System.out);


    public static void solve(int n, int p) {
        int k = 2 * n + p;
        int m = 0, node1 = 1, node2 = 2;
        while(m<k){
            m++;
            if(node2==n+1){
                node1++;
                node2=node1+1;
            }
            out.println(node1+" "+node2);
            node2++;
        }

    }


    public static void main(String[] args) {
        int t = in.nextInt();
        while (t-- > 0) {
            solve(in.nextInt(),in.nextInt());
        }

        out.close();
    }


    private static final class FastReader {
        private static BufferedReader BF;
        private static StringTokenizer ST;

        public FastReader() {
            BF = new BufferedReader(new InputStreamReader(System.in));
            ST = null;

        }


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

        }

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

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


}