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.awt.Point;
import java.io.*;
import java.math.BigInteger;
import java.util.*;

import javax.management.RuntimeErrorException;

import static java.lang.Math.*;

public class solver implements Runnable {

	BufferedReader in;
	PrintWriter out;
	StringTokenizer tok = new StringTokenizer("");

	void init() throws FileNotFoundException {
		in = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
	}

	String readString() throws IOException {
		while (!tok.hasMoreTokens()) {
			try {
				tok = new StringTokenizer(in.readLine());
			} catch (Exception e) {
				return null;
			}
		}
		return tok.nextToken();
	}

	int readInt() throws IOException {
		return Integer.parseInt(readString());
	}

	long readLong() throws IOException {
		return Long.parseLong(readString());
	}

	double readDouble() throws IOException {
		return Double.parseDouble(readString());
	}

	int[] readIntArr(int n, boolean sort, boolean reverse) throws IOException {
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = readInt();
		}
		if (sort)
			Arrays.sort(a);
		if (reverse) {
			int l = 0;
			int r = n - 1;
			while (l < r) {
				int t = a[l];
				a[l] = a[r];
				a[r] = t;
				l++;
				r--;
			}
		}
		return a;
	}

	int[] readIntArr(int n, boolean sort) throws IOException {
		return readIntArr(n, sort, false);
	}

	int[] readIntArr(int n) throws IOException {
		return readIntArr(n, false);
	}

	void printArray(Iterable<Integer> iterable) {
		for (int x : iterable) {
			out.print(x + " ");
		}
	}

	void printlnArray(Iterable<Integer> iterable) {
		for (int x : iterable) {
			out.println(x);
		}
	}

	public static void main(String[] args) {
		new Thread(null, new solver(), "", 256 * (1L << 20)).start();
	}

	long timeBegin, timeEnd;

	void time() {
		timeEnd = System.currentTimeMillis();
		System.err.println("Time = " + (timeEnd - timeBegin));
	}

	public void run() {
		try {
			timeBegin = System.currentTimeMillis();
			init();
			solve();
			out.close();
			// time();
		} catch (Exception e) {
			e.printStackTrace(System.err);
			System.exit(-1);
		}
	}

	ArrayList<Integer>[] graph;
	boolean[] vis;
	int[] h;

	void dfs(int x, int height) {
		vis[x] = true;
		h[x] = height;
		for (int y : graph[x]) {
			if (!vis[y])
				dfs(y, height + 1);
		}
	}

	class Container implements Comparable<Container> {
		int key;
		long value;

		public Container(int key, long value) {
			super();
			this.key = key;
			this.value = value;
		}

		@Override
		public int compareTo(Container o) {
			return o.value == value ? 0 : (o.value > value ? 1 : -1);
		}

	}

	void solve() throws IOException {
		int t = readInt();
		while (t-- > 0) {
			int n = readInt();
			int p = readInt();
			int cnt = 0;
			for (int i = 0; i < n; i++) {
				for (int j = i + 1; j < n; j++) {
					if (cnt < 2 * n + p) {
						out.println((i+1) + " " + (j+1));
						cnt++;
					}
				}
			}
		}
	}
}