#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int N = 2 * 1e5 + 10;
ll res;
ll a[N];
void solve() {
  ll n, p, ct = 0, tt;
  cin >> n >> p;
  tt = 2 * n + p;
  for (int i = 1; i <= n; ++i) {
    for (int j = i + 1; j <= n; ++j) {
      cout << i << " " << j << "\n";
      ++ct;
      if (ct == tt) return;
    }
  }
}
int main(int argc, char const *argv[]) {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  ll t = 1;
  cin >> t;
  while (t--) {
    solve();
  }
}

### Prompt

In CPP, your task is to solve the following problem:

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>
using namespace std;
using ll = long long;
const int N = 2 * 1e5 + 10;
ll res;
ll a[N];
void solve() {
  ll n, p, ct = 0, tt;
  cin >> n >> p;
  tt = 2 * n + p;
  for (int i = 1; i <= n; ++i) {
    for (int j = i + 1; j <= n; ++j) {
      cout << i << " " << j << "\n";
      ++ct;
      if (ct == tt) return;
    }
  }
}
int main(int argc, char const *argv[]) {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  ll t = 1;
  cin >> t;
  while (t--) {
    solve();
  }
}

```