#include <bits/stdc++.h>
using namespace std;
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long lcm(long long a, long long b) { return a * (b / gcd(a, b)); }
const double EPS = 1e-9;
const double PI = acos(-1.0);
const int INF = (1LL << 29);
using namespace std;
template <typename T>
string toString(T t) {
  stringstream ss;
  ss << t;
  return ss.str();
}
int main() {
  int t;
  cin >> t;
  for (int j = 0; j < t; j++) {
    int n, p;
    cin >> n >> p;
    set<pair<int, int> > edges;
    for (int i = 0; i < n; i++) {
      edges.insert({i, (i + 1) % n});
      edges.insert({i, (i - 1 + n) % n});
      edges.insert({i, (i + 2) % n});
      edges.insert({i, (i - 2 + n) % n});
    }
    set<pair<int, int> > out;
    for (auto e : edges) {
      if (out.count(e) == 0 && out.count({e.second, e.first}) == 0)
        out.insert(e);
    }
    for (int i = 0; i < n && p; i++)
      for (int j = 0; j < n && p; j++) {
        if (i != j)
          if (out.count({i, j}) == 0 && out.count({j, i}) == 0) {
            out.insert({i, j});
            p--;
          }
      }
    for (auto e : out) {
      cout << e.first + 1 << " " << e.second + 1 << endl;
    }
  }
  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>
using namespace std;
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long lcm(long long a, long long b) { return a * (b / gcd(a, b)); }
const double EPS = 1e-9;
const double PI = acos(-1.0);
const int INF = (1LL << 29);
using namespace std;
template <typename T>
string toString(T t) {
  stringstream ss;
  ss << t;
  return ss.str();
}
int main() {
  int t;
  cin >> t;
  for (int j = 0; j < t; j++) {
    int n, p;
    cin >> n >> p;
    set<pair<int, int> > edges;
    for (int i = 0; i < n; i++) {
      edges.insert({i, (i + 1) % n});
      edges.insert({i, (i - 1 + n) % n});
      edges.insert({i, (i + 2) % n});
      edges.insert({i, (i - 2 + n) % n});
    }
    set<pair<int, int> > out;
    for (auto e : edges) {
      if (out.count(e) == 0 && out.count({e.second, e.first}) == 0)
        out.insert(e);
    }
    for (int i = 0; i < n && p; i++)
      for (int j = 0; j < n && p; j++) {
        if (i != j)
          if (out.count({i, j}) == 0 && out.count({j, i}) == 0) {
            out.insert({i, j});
            p--;
          }
      }
    for (auto e : out) {
      cout << e.first + 1 << " " << e.second + 1 << endl;
    }
  }
  return 0;
}

```