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.util.*;

public class C {
    public static void main(String[] args) {
        FastScanner fs = new FastScanner();
        int t = fs.nextInt();
        for (int i=0;i<t;++i) {
            int n=fs.nextInt();
            int p=fs.nextInt();
            Set<Map.Entry<Integer, Integer>> g = new HashSet<>();
            Map<Integer, Integer> nedges = new HashMap<>();
            for (int a = 1; a <= n; a++) {
                for (int j=0; j < 2; j++) {
                    int minedge = -1;
                    int mincount = Integer.MAX_VALUE;
                    for (int b = 1; b <= n; b++) {
                        if (a != b && nedges.getOrDefault(b, 0) < mincount) {
                            mincount = nedges.getOrDefault(b, 0);
                            minedge = b;
                        }
                    }
                    nedges.put(a, nedges.getOrDefault(minedge, 0) + 1);
                    nedges.put(minedge, nedges.getOrDefault(minedge, 0) + 1);
                    g.add(new AbstractMap.SimpleImmutableEntry<>(Math.min(a, minedge), Math.max(a, minedge)));
                }
            }
            int ne = g.size();
            for (int a=1; a<=n && ne < 2*n+p; a++) {
                for (int b=1; b<=n && ne < 2*n+p; b++) {
                    if (a != b && g.add(new AbstractMap.SimpleImmutableEntry<>(Math.min(a, b), Math.max(a, b)))) {
                        ne++;
                    }
                }
            }
            for (Map.Entry<Integer, Integer> e : g) {
                System.out.println(e.getKey() + " " + e.getValue());
            }
        }
    }

    static long gcd(long a, long b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }

    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

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

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