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.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class CopyOfSolution {

    public static void main(final String[] args) throws NumberFormatException, IOException {
        final OutputStream outputStream = System.out;
        final PrintWriter out = new PrintWriter(outputStream);
        final InputReader in = new InputReader(System.in);
        final int t = in.nextInt();
        for (int i = 0; i < t; i++) {
            solve(in.nextInt(), in.nextInt(), out);
        }
        out.close();
    }

    private static void solve(final int n, final int p, final PrintWriter out) {
        final int[][] mat = new int[n + 1][n + 1];
        for (int i = 1; i < (n + 1); i++) {
            Arrays.fill(mat[i], 1);
            mat[i][i] = 0;
        }
        int rem = ((n * (n - 1)) >> 1) - (2 * n) - p;
        // uniform removal of edges
        // remove rem pairs
        for (int i = n; i > 0; i--) {
            for (int j = n; j > i; j--) {
                if (rem-- > 0) {
                    mat[i][j] = 0;
                } else {
                    break;
                }
            }
            if (rem <= 0) {
                break;
            }
        }
        for (int i = 1; i < (n + 1); i++) {
            for (int j = i + 1; j < (n + 1); j++) {
                if (mat[i][j] == 1) {
                    out.println(i + " " + j);
                }
            }
        }
    }

    private static class InputReader {
        private final BufferedReader reader;
        private StringTokenizer s;

        public InputReader(final InputStream is) {
            final InputStreamReader in = new InputStreamReader(is);
            final BufferedReader reader = new BufferedReader(in);
            this.reader = reader;
        }

        public String next() {
            while ((this.s == null) || !this.s.hasMoreTokens()) {
                try {
                    this.s = new StringTokenizer(this.reader.readLine());
                } catch (final Exception e) {
                    throw new RuntimeException(e);
                }
            }
            return this.s.nextToken();
        }

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

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

}