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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import java.util.StringTokenizer;

/**
 * @author Jens Staahl
 */

public class Prac {

	// some local config
	// static boolean test = false ;
	private boolean test = System.getProperty("ONLINE_JUDGE") == null;
	static String testDataFile = "testdata.txt";
	// static String testDataFile = "testdata.txt";
	private static String ENDL = "\n";
	// Just solves the acutal kattis-problem
	ZKattio io;
	
	private void solve() throws Throwable {
		io = new ZKattio(stream);

		int t = io.getInt();
		for (int i = 0; i < t; i++) {
			solveIt();
		}
		out.flush();
	}

	private void solveIt() {
		int n = io.getInt(), p = io.getInt();
		int num = 2*n + p;
		int reach = 1;
		int i = 0;
		while (num > 0) {
			if(i+reach <n) {
				out.println((i+1) + " " + (i + reach + 1));
				num--;
				i ++;
			} else {
				i = 0;
				reach ++;
			}
		}
	}

	public static void main(String[] args) throws Throwable {
		new Prac().solve();
	}

	public Prac() throws Throwable {
		if (test) {
			stream = new FileInputStream(testDataFile);
		}
	}

	InputStream stream = System.in;
	PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));// outStream

	public class ZKattio extends PrintWriter {
		public ZKattio(InputStream i) {
			super(new BufferedOutputStream(System.out));
			r = new BufferedReader(new InputStreamReader(i));
		}

		public ZKattio(InputStream i, OutputStream o) {
			super(new BufferedOutputStream(o));
			r = new BufferedReader(new InputStreamReader(i));
		}

		public boolean hasMoreTokens() {
			return peekToken() != null;
		}

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

		public double getDouble() {
			return Double.parseDouble(nextToken());
		}

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

		public String getWord() {
			return nextToken();
		}

		private BufferedReader r;
		private String line;
		private StringTokenizer st;
		private String token;

		private String peekToken() {
			if (token == null)
				try {
					while (st == null || !st.hasMoreTokens()) {
						line = r.readLine();
						if (line == null)
							return null;
						st = new StringTokenizer(line);
					}
					token = st.nextToken();
				} catch (IOException e) {
				}
			return token;
		}

		private String nextToken() {
			String ans = peekToken();
			token = null;
			return ans;
		}
	}
	// System.out;

}