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.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main {

	final static int mod = 1_000_000_007;
	
	public static void main(String[] args) throws Exception {

		STDIN scan = new STDIN();
		PrintWriter pw = new PrintWriter(System.out);
		
		int t = scan.nextInt();
		while(t-- > 0) {
			int n = scan.nextInt(), p = scan.nextInt(), k = 2*n + p;
			for(int i = 1; i < n; i++) pw.println(i + " " + (i+1));
			k -= (n-1);
			for(int i = 1; i <= n && k > 0; i++)
				for(int j = i+2; j <= n && k > 0; j++, k--)
					pw.println(i + " " + j);
		}
		pw.flush();
	
	}

	
	static class STDIN {
		BufferedReader br;
		StringTokenizer st;

		public STDIN() {
			br = new BufferedReader(new InputStreamReader(System.in));
			st = null;
		}
		
		boolean hasNext() throws Exception {
			if(!st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
			return st.hasMoreTokens();
		}

		int nextInt() throws Exception {
			return Integer.parseInt(next());
		}

		long nextLong() throws Exception {
			return Long.parseLong(next());
		}

		double nextDouble() throws Exception {
			return Double.parseDouble(next());
		}

		String next() throws Exception {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		String nextLine() throws Exception {
			return br.readLine();
		}
	}
}