#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC target("avx2")
#pragma GCC optimize("unroll-loops")
using namespace std;
template <class T>
ostream& operator<<(ostream& os, vector<T> V) {
  os << "[ ";
  for (auto v : V) os << v << " ";
  return os << "]";
}
template <typename T>
void __printer(const char* var_name, T&& val) {
  cerr << var_name << " = " << val << endl;
}
template <typename T, typename... Arguments>
void __printer(const char* arg_names, T&& val, Arguments&&... remaining_args) {
  const char* comma = strchr(arg_names + 1, ',');
  cerr.write(arg_names, comma - arg_names) << " = " << val << ", ";
  __printer(comma + 1, remaining_args...);
}
template <typename T>
using min_heap = priority_queue<T, vector<T>, greater<T>>;
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  long long int _ = 1;
  cin >> _;
  while (_--) {
    long long int n, k;
    cin >> n >> k;
    long long int c = 2 * n + k;
    for (long long int i = 1; i <= n; ++i) {
      for (long long int j = i + 1; j <= n; ++j) {
        if (i != j) {
          cout << i << " " << j << '\n';
          c--;
        }
        if (c == 0) break;
      }
      if (c == 0) break;
    }
  }
  return 0;
}

### Prompt

Develop a solution in Cpp to the problem described below:

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

### Response

```cpp
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC target("avx2")
#pragma GCC optimize("unroll-loops")
using namespace std;
template <class T>
ostream& operator<<(ostream& os, vector<T> V) {
  os << "[ ";
  for (auto v : V) os << v << " ";
  return os << "]";
}
template <typename T>
void __printer(const char* var_name, T&& val) {
  cerr << var_name << " = " << val << endl;
}
template <typename T, typename... Arguments>
void __printer(const char* arg_names, T&& val, Arguments&&... remaining_args) {
  const char* comma = strchr(arg_names + 1, ',');
  cerr.write(arg_names, comma - arg_names) << " = " << val << ", ";
  __printer(comma + 1, remaining_args...);
}
template <typename T>
using min_heap = priority_queue<T, vector<T>, greater<T>>;
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  long long int _ = 1;
  cin >> _;
  while (_--) {
    long long int n, k;
    cin >> n >> k;
    long long int c = 2 * n + k;
    for (long long int i = 1; i <= n; ++i) {
      for (long long int j = i + 1; j <= n; ++j) {
        if (i != j) {
          cout << i << " " << j << '\n';
          c--;
        }
        if (c == 0) break;
      }
      if (c == 0) break;
    }
  }
  return 0;
}

```