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 javafx.util.Pair;

import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintStream;
import java.io.PrintWriter;
import java.lang.reflect.Array;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Objects;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * Created by timur on 28.03.15.
 */

public class TaskC {
    boolean eof;
    BufferedReader br;
    StringTokenizer st;
    PrintWriter out;

    public static void main(String[] args) throws IOException {
        new TaskC().run();
    }

    public String nextToken() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                eof = true;
                return "-1";
            }
        }
        return st.nextToken();
    }

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

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

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

    String nextLine() throws IOException {
        return br.readLine();
    }


    void run() throws IOException {
        InputStream input = System.in;
        PrintStream output = System.out;
        try {
            File f = new File("a.in");
            if (f.exists() && f.canRead()) {
                input = new FileInputStream(f);
                output = new PrintStream("a.out");
            }
        } catch (Throwable e) {
        }
        br = new BufferedReader(new InputStreamReader(input));
        out = new PrintWriter(output);
        solve();
        br.close();
        out.close();
    }

    long rec(long N, long K) {
        if(N<K || N<1 || K<1)
            return 0;
        if(N==K)
            return 1;
        if(K==1)
            return N;
        return rec(N-1, K-1) + rec(N-1, K);
    }

    int gcd (int a, int b) {
        if (b == 0)
            return a;
        else
            return gcd (b, a % b);
    }
    
    void solve() {
        int t = nextInt();
        for (int i = 0; i < t; i++) {
            int n = nextInt(), p = nextInt(), cnt = 0;
            for (int j = 0; j < n && cnt < 2 * n + p; j++) {
                for (int k = j + 1; k < n && cnt < 2 * n + p; k++) {
                    out.println((j + 1) + " " + (k + 1));
                    cnt++;
                }
            }
        }
    }
}