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.*;
import java.awt.Point;

public class A {
  public static void main(String[] args) {
    Scanner in = new Scanner(System.in);
    int T = in.nextInt();
    for(int cas=0; cas<T; cas++) {
      int n = in.nextInt();
      int p = in.nextInt();

      E = new HashSet<Point>();

      for(int i=0; i<n; i++)
        addEdge(i, (i+1)%n);
      for(int i=0; i<n; i++)
        addEdge(i, (i+2)%n);
      while(E.size() < 2*n+p) {
        int x = r(0, n-1);
        int y = r(0, n-1);
        addEdge(x, y);
      }

      for(Point e : E) {
        System.out.println((e.x+1) + " " + (e.y+1));
      }
    }
  }

  static int r(int lo, int hi) {
    return lo + (int)(Math.random()*(hi-lo+1));
  }

  static Set<Point> E;
  static void addEdge(int x, int y) {
    if(x==y) return;
    if(x > y) {
      addEdge(y, x);
    } else {
      E.add(new Point(x, y));
    }
  }
}
