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.StringTokenizer;

public class CR234_searching_for_graph {

    public static void main(String... args) throws IOException {
        MyScanner sc = new MyScanner();
        int t = sc.nextInt();
        
        _nextTest:
        for (int tt = 0; tt < t; tt++) {
            int n = sc.nextInt();
            int p = sc.nextInt();

            boolean[][] g = new boolean[n][n];
            int prevNode = 0;
            for (int i = 0; i < n; i++) {
                int nextNode = (prevNode + 1) % n;
                System.out.println((prevNode + 1) + " " + (nextNode + 1));
                g[prevNode][nextNode] = g[nextNode][prevNode] = true;
                prevNode = nextNode;
            }
            prevNode = 0;
            for (int i = 0; i < n; i++) {
                int nextNode = (prevNode + 2) % n;
                if (g[prevNode][nextNode]) {
                    prevNode = (prevNode + 1) % n;
                    nextNode = (prevNode + 2) % n;
                }
                System.out.println((prevNode + 1) + " " + (nextNode + 1));
                g[prevNode][nextNode] = g[nextNode][prevNode] = true;
                prevNode = nextNode;
            }

            int c = 0;
            for (int i = 0; i < n; i++) {
                for (int j = i+1; j < n; j++) {
                    if (c == p) {
                        continue _nextTest;
                    }
                    if (!g[i][j]) {
                        g[i][j] = g[j][i] = true;
                        System.out.println((i + 1) + " " + (j + 1));
                        c++;
                    }
                }
            }
        }
    }

    static class MyScanner {

        BufferedReader br;
        StringTokenizer st;

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

        public String next() throws IOException {
            if (st == null || !st.hasMoreTokens()) {
                String line = br.readLine();
                while (line.isEmpty()) {
                    line = br.readLine();
                }
                st = new StringTokenizer(line);
            }
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            String next = next();
            return Integer.parseInt(next);
        }

        private long nextLong() throws IOException {
            String next = next();
            return Long.parseLong(next);
        }
    }
}
