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
#include <bits/stdc++.h>
using namespace std;
int main(int argc, char* argv[]) {
  ios_base::sync_with_stdio(false);
  int n, p, t;
  cin >> t;
  for (; t > 0; --t) {
    cin >> n >> p;
    int edges = n + n + p;
    vector<int> degree(n, 0);
    vector<vector<bool>> con(n, vector<bool>(n, false));
    for (int e = 0; e < edges; ++e) {
      int low = 999999;
      int index = 0;
      for (int i = 0; i < n; ++i) {
        if (degree[i] < low) {
          low = degree[i];
          index = i;
        }
      }
      int index_b = 0;
      if (index == 0) index_b = 1;
      low = 9999999;
      for (int i = 0; i < n; ++i) {
        if (i == index) continue;
        if (con[i][index]) continue;
        if (degree[i] < low) {
          low = degree[i];
          index_b = i;
        }
      }
      cout << index + 1 << " " << index_b + 1 << endl;
      con[index][index_b] = con[index_b][index] = true;
      degree[index]++;
      degree[index_b]++;
    }
  }
  return EXIT_SUCCESS;
}
