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;
template <typename T>
inline T abs(T a) {
  return ((a < 0) ? -a : a);
}
template <typename T>
inline T sqr(T a) {
  return a * a;
}
const int N = 100009;
const int MOD = 1e9 + 7;
const int INF = 1e9;
const long long INF64 = 2e18;
const long double PI = 3.1415926535897932384626433832795;
const long double eps = 1e-9;
int main() {
  srand(time(NULL));
  cout << setprecision(10) << fixed;
  cerr << setprecision(10) << fixed;
  int t;
  cin >> t;
  for (int _ = 0; _ < (int)(t); ++_) {
    int n, p;
    cin >> n >> p;
    vector<pair<int, int> > edges;
    for (int i = 0; i < (int)(n); ++i)
      edges.push_back(make_pair(i, (i + 1) % n));
    for (int i = 0; i < (int)(n); ++i)
      edges.push_back(make_pair(i, (i + 2) % n));
    int d = 0;
    while (p > 0) {
      for (int i = 0; i < (int)(min(p, n)); ++i)
        edges.push_back(make_pair(i, (i + 3 + d) % n));
      p -= n;
      ++d;
    }
    for (int i = 0; i < (int)((int)(edges.size())); ++i)
      cout << edges[i].first + 1 << ' ' << edges[i].second + 1 << endl;
  }
  return 0;
}
