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.*;
import java.util.*;
import java.lang.reflect.*;


public class Main {

	static long CURRENT_TIME_NANO = System.nanoTime();

	public static void main(String[] args) throws Exception {
		
		int tests = next();

		for (int test = 0; test < tests; test++) {
			int n = next();
			int p = next();
			boolean[][] con = new boolean[n][n];

			for (int i = 0; i < n; i++)
				con[i][(i + 1) % n] = true;

			for (int i = 0; i < n; i++)
				con[i][(i + 2) % n] = true;

			for (int i = 0; i < n; i++)
				for (int j = 0; j < n; j++)
					if (con[i][j]) con[j][i] = true;

			for (int i = 0; i < n && p > 0; i++)
				for (int j = 0; j < i && p > 0; j++) {
					if (!con[i][j]) {
						p--;
						con[i][j] = con[j][i] = true;
					}
				}

		   	for (int i = 0; i < n; i++)
		   		for (int j = 0; j < i; j++)
		   			if (con[i][j]) out.println((i + 1) + " " + (j + 1));

		}

		out.close();
	}
	
	static void printtime() {System.out.println((System.nanoTime() - CURRENT_TIME_NANO)*1e-9);}
	static void nexttime() {printtime(); CURRENT_TIME_NANO = System.nanoTime();}
	static PrintWriter out = new PrintWriter(System.out);
	
	static BufferedReader bufferedreader = new BufferedReader(new InputStreamReader(System.in));
	static StringTokenizer in = new StringTokenizer("");

	static String nextToken() throws Exception {
		if (!in.hasMoreTokens()) in = new StringTokenizer(bufferedreader.readLine());
		return in.nextToken();
	}

	static int next()  throws Exception {return Integer.parseInt(nextToken());};
	static int[] next(int n) throws Exception {
		int[] x = new int[n];
		for (int i = 0; i < n; i++) x[i] = next();
		return x;
	}
	static int[][] next(int n, int m) throws Exception {
		int[][] x = new int[n][];
		for (int i = 0; i < n; i++) x[i] = next(m);
		return x;
	}

	static long nextl() throws Exception {return Long.parseLong(nextToken());};
	static long[] nextl(int n) throws Exception {
		long[] x = new long[n];
		for (int i = 0; i < n; i++) x[i] = nextl();
		return x;
	}
	static long[][] nextl(int n, int m) throws Exception {
		long[][] x = new long[n][];
		for (int i = 0; i < n; i++) x[i] = nextl(m);
		return x;
	}

	static double nextd() throws Exception {return Double.parseDouble(nextToken());};
	static double[] nextd(int n) throws Exception {
		double[] x = new double[n];
		for (int i = 0; i < n; i++) x[i] = nextd();
		return x;
	}
	static double[][] nextd(int n, int m) throws Exception {
		double[][] x = new double[n][];
		for (int i = 0; i < n; i++) x[i] = nextd(m);
		return x;
	}

	static String nextline() throws Exception {
		in = new StringTokenizer("");
		return bufferedreader.readLine();
	}

	static void sout(long x) {System.out.println(x);}
	static void sout(String s) {System.out.println(s);}
	static void sout(int[] x) {for (int xx : x) System.out.print(xx + " "); System.out.println();}
	static void sout(long[] x) {for (long xx : x) System.out.print(xx + " "); System.out.println();}
	static void sout(int[][] x) {for (int[] xx : x) sout(xx); System.out.println();}
	static void sout(long[][] x) {for (long[] xx : x) sout(xx); System.out.println();}
	static void sout(int[][][] x) {for (int[][] xx : x) sout(xx); System.out.println();}
	static void sout(long[][][] x) {for (long[][] xx : x) sout(xx); System.out.println();}


}