#include <bits/stdc++.h>
using namespace std;
int a[100][100];
int main() {
  int i, j;
  int t;
  cin >> t;
  while (t--) {
    int n, p;
    memset(a, 0, sizeof(a));
    cin >> n >> p;
    int sum = 0;
    p += 2 * n;
    while (sum < p) {
      if (sum == p) break;
      for (int k = 1; k <= n; k++) {
        if (sum == p) break;
        for (i = 1; i <= n; i++) {
          if (sum == p) break;
          j = i + k;
          j %= n;
          if (j == 0) j = n;
          while (j != i) {
            if (a[j][i]) break;
            a[j][i] = a[i][j] = 1;
            sum++;
            if (sum == p) break;
          }
          if (sum == p) break;
        }
        if (sum == p) break;
      }
      if (sum == p) break;
    }
    for (i = 1; i <= n; i++) {
      for (j = i + 1; j <= n; j++)
        if (a[i][j]) cout << i << " " << j << endl;
    }
  }
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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;
int a[100][100];
int main() {
  int i, j;
  int t;
  cin >> t;
  while (t--) {
    int n, p;
    memset(a, 0, sizeof(a));
    cin >> n >> p;
    int sum = 0;
    p += 2 * n;
    while (sum < p) {
      if (sum == p) break;
      for (int k = 1; k <= n; k++) {
        if (sum == p) break;
        for (i = 1; i <= n; i++) {
          if (sum == p) break;
          j = i + k;
          j %= n;
          if (j == 0) j = n;
          while (j != i) {
            if (a[j][i]) break;
            a[j][i] = a[i][j] = 1;
            sum++;
            if (sum == p) break;
          }
          if (sum == p) break;
        }
        if (sum == p) break;
      }
      if (sum == p) break;
    }
    for (i = 1; i <= n; i++) {
      for (j = i + 1; j <= n; j++)
        if (a[i][j]) cout << i << " " << j << endl;
    }
  }
}

```