#include <bits/stdc++.h>
template <typename T>
T pow(T a, T b, long long m) {
  T ans = 1;
  while (b > 0) {
    if (b % 2 == 1) ans = (ans * a) % m;
    b /= 2;
    a = (a * a) % m;
  }
  return ans % m;
}
using namespace std;
const long long N = 2e5 + 77;
long long A[N];
void sol() {
  long long n, p;
  cin >> n >> p;
  long long g[n + 1][n + 1];
  memset(g, 0, sizeof(g));
  long long c = 2 * n + p;
  vector<pair<long long, long long> > Ans;
  for (long long(i) = (1); (i) < (n + 1); (i)++) {
    for (long long(j) = (1); (j) < (n + 1); (j)++) {
      if (i == j) continue;
      if (g[i][j] == 0 && c > 0) {
        g[i][j] = g[j][i] = 1;
        c--;
        Ans.push_back({i, j});
      }
    }
  }
  for (auto i : Ans) cout << i.first << ' ' << i.second << '\n';
}
int32_t main() {
  long long t;
  cin >> t;
  while (t--) sol();
  return 0;
}

### Prompt

Create a solution in Cpp for 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>
template <typename T>
T pow(T a, T b, long long m) {
  T ans = 1;
  while (b > 0) {
    if (b % 2 == 1) ans = (ans * a) % m;
    b /= 2;
    a = (a * a) % m;
  }
  return ans % m;
}
using namespace std;
const long long N = 2e5 + 77;
long long A[N];
void sol() {
  long long n, p;
  cin >> n >> p;
  long long g[n + 1][n + 1];
  memset(g, 0, sizeof(g));
  long long c = 2 * n + p;
  vector<pair<long long, long long> > Ans;
  for (long long(i) = (1); (i) < (n + 1); (i)++) {
    for (long long(j) = (1); (j) < (n + 1); (j)++) {
      if (i == j) continue;
      if (g[i][j] == 0 && c > 0) {
        g[i][j] = g[j][i] = 1;
        c--;
        Ans.push_back({i, j});
      }
    }
  }
  for (auto i : Ans) cout << i.first << ' ' << i.second << '\n';
}
int32_t main() {
  long long t;
  cin >> t;
  while (t--) sol();
  return 0;
}

```