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.IOException;
import java.util.InputMismatchException;
import java.io.PrintStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author karan173
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        solver.solve(1, in, out);
        out.close();
    }
}

class TaskA
{
    public void solve(int testNumber, FastReader in, PrintWriter out)
    {
        int t = in.ni ();
        while (t-- > 0)
        {
            int n = in.ni ();
            int p = in.ni ();
            boolean adj[][] = new boolean[n][n];
            for (int i = 0; i < n; i++)
            {
                for (int j = 0; j < n; j++)
                {
                    adj[i][j] = false;
                }
            }
            int cnt = 0;
            for (int i = 0; i < 5; i++)
            {
                for (int j = i + 1; j < 5; j++)
                {
                    if (cnt == 10 + p)
                    {
                        break;
                    }
                    adj[i][j] = true;
                    adj[j][i] = true;
                    cnt++;
                }
                if (cnt == 10 + p)
                {
                    break;
                }
            }
            int ctr = 0;
            for (int i = 5; i < n; i++)
            {
                adj[i][ctr] = true;
                adj[ctr][i] = true;
                ctr = (ctr + 1) % 5;
                adj[i][ctr] = true;
                adj[ctr][i] = true;
                ctr = (ctr + 1) % 5;
                cnt += 2;
            }

//            for (int i = 5; i < n; i++)
//            {
//                for (int j = 0; j < 5; j++)
//                {
//                    if (cnt == 2 * n + p)
//                    {
//                        break;
//                    }
//                    if (adj[i][j])
//                    {
//                        continue;
//                    }
//                    adj[i][j] = adj[j][i] = true;
//                    cnt++;
//                }
//                if (cnt == 2 * n + p)
//                {
//                    break;
//                }
//            }
            cnt = 0;
            for (int i = 0; i < n; i++)
            {
                for (int j = i + 1; j < n; j++)
                {
                    if (adj[i][j])
                    {
                        cnt++;
                    }
                }
            }
            if (cnt > 2 * n + p)
            {
                throw new RuntimeException ();
            }
            for (int i = 5; i < n; i++)
            {
                for (int j = i + 1; j < n; j++)
                {
                    if (cnt == 2 * n + p)
                    {
                        break;
                    }
                    if (adj[i][j])
                    {
                        continue;
                    }
                    adj[i][j] = adj[j][i] = true;
                    cnt++;
                }
                if (cnt == 2 * n + p)
                {
                    break;
                }
            }
            for (int i = 0; i < n; i++)
            {
                for (int j = i + 1; j < n; j++)
                {
                    if (cnt == 2 * n + p)
                    {
                        break;
                    }
                    if (adj[i][j])
                    {
                        continue;
                    }
                    adj[i][j] = adj[j][i] = true;
                    cnt++;
                }
                if (cnt == 2 * n + p)
                {
                    break;
                }
            }
            int netCnt = 0;
            for (int i = 0; i < n; i++)
            {
                for (int j = i + 1; j < n; j++)
                {
                    if (adj[i][j])
                    {
                        out.println ((i + 1) + " " + (j + 1));
                        netCnt++;
                    }
                }
            }
            if (netCnt != 2 * n + p)
            {
                for (double x = 1; x < Double.MAX_VALUE; x++)
                {

                }
            }
        }
    }
}

class FastReader
{

    public InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;

    public FastReader(InputStream stream)
    {
        this.stream = stream;
    }

    public int read()
    {
        if (numChars == -1)
        {
            throw new InputMismatchException ();
        }
        if (curChar >= numChars)
        {
            curChar = 0;
            try
            {
                numChars = stream.read (buf);
            } catch (IOException e)
            {
                throw new InputMismatchException ();
            }
            if (numChars <= 0)
            {
                return -1;
            }
        }
        return buf[curChar++];
    }

    public int ni()
    {
        int c = read ();
        while (isSpaceChar (c))
            c = read ();
        int sgn = 1;
        if (c == '-')
        {
            sgn = -1;
            c = read ();
        }
        int res = 0;
        do
        {
            if (c < '0' || c > '9')
            {
                throw new InputMismatchException ();
            }
            res *= 10;
            res += c - '0';
            c = read ();
        } while (!isSpaceChar (c));
        return res * sgn;
    }

    public boolean isSpaceChar(int c)
    {
        if (filter != null)
        {
            return filter.isSpaceChar (c);
        }
        return isWhitespace (c);
    }

    public static boolean isWhitespace(int c)
    {
        return c==' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public interface SpaceCharFilter
    {
        public boolean isSpaceChar(int ch);
    }
}
