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.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.PriorityQueue;
import java.util.Stack;
import java.util.StringTokenizer;

public class Main {

	public static void main(String[] args) throws IOException 
	{
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		StringBuilder sb = new StringBuilder();
		while(t-->0)
		{
			int n = sc.nextInt() , p = sc.nextInt();
			PriorityQueue<Node> q = new PriorityQueue<Node>();
			boolean[][] mat = new boolean[n][n];
			for (int i = 0; i < n; i++) 
			{
				q.add(new Node(i,0));
				mat[i][i] = true;
			}
			int edges = 2*n+p;
			while(edges>0)
			{
				Node u = q.poll() ;
				Node v = null;
				Stack<Node> stak = new Stack<Node>();
				
				boolean found = false;
				while(!q.isEmpty())
				{
					v = q.poll();
					if(!mat[u.idx][v.idx])
					{
						found = true;
						break;
					}
					stak.push(v);
				}
				q.addAll(stak);
				if(!found){
					q.add(u);
					continue;
				}
				sb.append((1+u.idx)+" "+(v.idx+1)+"\n");
				++u.deg;
				++v.deg;
				mat[u.idx][v.idx] = mat[v.idx][u.idx] = true;
				edges--;
				q.add(v);
				q.add(u);
			}
		}
		System.out.print(sb);
	}
	
	static class Node implements Comparable<Node>
	{
		int idx,deg;
		public Node(int a,int b) {
			idx = a;deg = b;
		}
		
		public int compareTo(Node o) {
			return deg-o.deg;
		}
	}
	
	
	static class Scanner 
	{
		StringTokenizer st;
		BufferedReader br;
		public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}
		public Scanner(String s) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(s));
		}
		public String next() throws IOException 
		{
			while (st == null || !st.hasMoreTokens()) 
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public int nextInt() throws IOException {return Integer.parseInt(next());}
		public String nextLine() throws IOException {return br.readLine();}		
		public long nextLong() throws IOException {return Long.parseLong(next());}		
		public double nextDouble() throws IOException {return Double.parseDouble(next());}	
		public boolean ready() throws IOException {return br.ready();}
		public int[] nextIntArr() throws IOException{
			st = new StringTokenizer(br.readLine());
			int[] res = new int[st.countTokens()];
			for (int i = 0; i < res.length; i++) 
				res[i] = Integer.parseInt(st.nextToken());
			
			return res;
		}
		public char[] nextCharArr() throws IOException{
			st = new StringTokenizer(br.readLine());
			char[] res = new char[st.countTokens()];
			for (int i = 0; i < res.length; i++) 
				res[i] = st.nextToken().charAt(0);
			
			return res;
		}
	}	
	
}