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 {
	public static void main(String[] args) throws Exception{
		int t = readInt();
		while(t-- > 0){
			int n = readInt();
			int p = readInt();
			int[][] mat = new int[n][n];
			for(int i = 0; i < n; i++){
				mat[i][(i+1)%n] = 1;
				mat[i][(i+2)%n] = 1;
				mat[(i+1)%n][i] = 1;
				mat[(i+2)%n][i] = 1;
			}
			while(p-- > 0){
				label:
				for(int i = 0; i < n; i++){
					for(int j = i+1; j < n; j++){
						if(mat[i][j] == 0){
							mat[i][j] = 1;
							mat[j][i] = 1;
							break label;
						}
					}
				}
			}
			for(int i = 0; i < n; i++){
				for(int j = i+1; j < n; j++){
					if(mat[i][j] == 1){
						System.out.println((i+1) + " " + (j+1));
					}
				}
			}
		}
	}
	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());
	}
	static long readLong() throws Exception {
		return Long.parseLong(readString());
	}
}
