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.util.ArrayList;
import java.util.Scanner;

public class A {
	public static void main(String[] args) {
		solve();
	}
	public static void check() {
		for(int n=5;n<=24;n++) {
			for(int p=0;2*n+p<=n*(n-1)/2;p++) {
				if (verify(solve(n,p), n, p)) {
					System.out.println("ok:" + n + "," + p);
				}else{
					System.out.println("failed:" + n + "," + p);
					return;
				}
			}
		}		
	}
	public static void solve() {
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		for(int i=0;i<t;i++) {
			int n = sc.nextInt();
			int p = sc.nextInt();
			ArrayList<Edge> ans = solve(n,p);
			for(Edge e:ans) {
				System.out.println(e.u + " " + e.v);
			}
		}		
	}
	public static ArrayList<Edge> solve(int n,int p) {
		ArrayList<Edge> ans = new ArrayList<>();
		int e = n * 2 + p;
		for(int i=0;i<n/2;i++) {
			for(int j=0;j<n;j++) {
				ans.add(new Edge(j+1,(j+i+1)%n+1));
				e--;
				if (e<=0) {
					return ans;
				}
			}
		}
		if (n%2==0) {
			for(int i=0;i<n/2;i++) {
				ans.add(new Edge(i+1,i+n/2+1));
				e--;
				if (e<=0) {
					return ans;
				}
			}
		}
		return ans;
	}
	public static boolean verify (ArrayList<Edge> ans,int n,int p) {
		for(long i=1;i<(1<<n);i++) {
			int k = Long.bitCount(i);
			int count = 0;
			for(Edge e:ans) {
				if ((i & (1<<e.u)) * (i & (1<<e.v)) != 0) {
					count++;
				}
			}
			if (count > 2 * k + p) {
				return false;
			}
		}
		return true;
	}
}
class Edge {
	int u;
	int v;
	public Edge(int u,int v) {
		this.u = u;
		this.v = v;
	}
}