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.util.StringTokenizer;


public class A {
	static BufferedReader stdin = new BufferedReader(new InputStreamReader(System.in));
	static StringTokenizer st = new StringTokenizer("");
	
	static String readString() throws Exception {
		while(!st.hasMoreTokens())
			st = new StringTokenizer(stdin.readLine());
		return st.nextToken();
	}

	static int readInt() throws Exception {
		return Integer.parseInt(readString());
	}
	
	public static void main(String[] args) throws Exception{
		int t = readInt();
		while(t-- > 0){
			
			int n = readInt();
			int p = readInt();
			boolean adj[][] = new boolean[n+1][n+1];
			for(int i = 1; i <= n; i++){
				int from = i;
				int to = (i+1)%(n+1);
				if(to < i+1) to += 1;
				adj[from][to] = true;
				adj[to][from] = true;
//				System.out.println("la til "+from+" til "+to);
				 to = (i+2)%(n+1);
					if(to < i+2) to += 1;
				adj[from][to] = true;
				adj[to][from] = true;
//				System.out.println("la til "+from+" til "+to);
			}
			int step = 3;
			while(p > 0){
				for(int i = 1; i <= n; i++){
					int from = i;
					int to = (i+step)%(n+1);
					if(to < i+step) to += 1;
					adj[from][to] = true;
					adj[to][from] = true;
//					System.out.println("la til "+from+" til "+to);
					p--;
					if(p == 0) break;
				}
				step++;
			}
			boolean print[][] = new boolean[n+1][n+1];
			for(int i = 1; i <= n; i++){
				for(int j = 1; j<= n; j++){
					if(adj[i][j] && !print[i][j]){
						System.out.println(i+" "+j);
						print[i][j] = true;
						print[j][i] = true;
					}
				}
			}
			
		}
	}

}
