#include <bits/stdc++.h>
using namespace std;
int64_t MOD;
inline void normal(int64_t &a) {
  a %= MOD;
  (a < 0) && (a += MOD);
}
inline int64_t modMul(int64_t a, int64_t b) {
  a %= MOD, b %= MOD;
  normal(a), normal(b);
  return (a * b) % MOD;
}
inline int64_t modAdd(int64_t a, int64_t b) {
  a %= MOD, b %= MOD;
  normal(a), normal(b);
  return (a + b) % MOD;
}
inline int64_t modSub(int64_t a, int64_t b) {
  a %= MOD, b %= MOD;
  normal(a), normal(b);
  a -= b;
  normal(a);
  return a;
}
inline int64_t modPow(int64_t b, int64_t p) {
  int64_t r = 1;
  while (p) {
    if (p & 1) r = modMul(r, b);
    b = modMul(b, b);
    p >>= 1;
  }
  return r;
}
inline int64_t modInverse(int64_t a) { return modPow(a, MOD - 2); }
inline int64_t modDiv(int64_t a, int64_t b) { return modMul(a, modInverse(b)); }
template <typename F, typename S>
ostream &operator<<(ostream &os, const pair<F, S> &p) {
  return os << "(" << p.first << ", " << p.second << ")";
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  os << "{";
  typename vector<T>::const_iterator it;
  for (it = v.begin(); it != v.end(); it++) {
    if (it != v.begin()) os << ", ";
    os << *it;
  }
  return os << "}";
}
template <typename T>
ostream &operator<<(ostream &os, const set<T> &v) {
  os << "[";
  typename set<T>::const_iterator it;
  for (it = v.begin(); it != v.end(); it++) {
    if (it != v.begin()) os << ", ";
    os << *it;
  }
  return os << "]";
}
template <typename F, typename S>
ostream &operator<<(ostream &os, const map<F, S> &v) {
  os << "[";
  typename map<F, S>::const_iterator it;
  for (it = v.begin(); it != v.end(); it++) {
    if (it != v.begin()) os << ", ";
    os << it->first << " = " << it->second;
  }
  return os << "]";
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  ;
  int64_t t = 1;
  cin >> t;
  for (int64_t trr = 1; trr <= t; trr++) {
    int64_t n, p;
    cin >> n >> p;
    vector<pair<int64_t, int64_t> > vec;
    for (int64_t i = 1; i <= n; i++) {
      for (int64_t j = i + 1; j <= n; j++) {
        vec.push_back({i, j});
      }
    }
    for (int64_t i = 0; i < 2 * n + p; i++) {
      cout << vec[i].first << " " << vec[i].second << endl;
    }
  }
}

### Prompt

Your challenge is to write a Cpp solution to 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;
int64_t MOD;
inline void normal(int64_t &a) {
  a %= MOD;
  (a < 0) && (a += MOD);
}
inline int64_t modMul(int64_t a, int64_t b) {
  a %= MOD, b %= MOD;
  normal(a), normal(b);
  return (a * b) % MOD;
}
inline int64_t modAdd(int64_t a, int64_t b) {
  a %= MOD, b %= MOD;
  normal(a), normal(b);
  return (a + b) % MOD;
}
inline int64_t modSub(int64_t a, int64_t b) {
  a %= MOD, b %= MOD;
  normal(a), normal(b);
  a -= b;
  normal(a);
  return a;
}
inline int64_t modPow(int64_t b, int64_t p) {
  int64_t r = 1;
  while (p) {
    if (p & 1) r = modMul(r, b);
    b = modMul(b, b);
    p >>= 1;
  }
  return r;
}
inline int64_t modInverse(int64_t a) { return modPow(a, MOD - 2); }
inline int64_t modDiv(int64_t a, int64_t b) { return modMul(a, modInverse(b)); }
template <typename F, typename S>
ostream &operator<<(ostream &os, const pair<F, S> &p) {
  return os << "(" << p.first << ", " << p.second << ")";
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  os << "{";
  typename vector<T>::const_iterator it;
  for (it = v.begin(); it != v.end(); it++) {
    if (it != v.begin()) os << ", ";
    os << *it;
  }
  return os << "}";
}
template <typename T>
ostream &operator<<(ostream &os, const set<T> &v) {
  os << "[";
  typename set<T>::const_iterator it;
  for (it = v.begin(); it != v.end(); it++) {
    if (it != v.begin()) os << ", ";
    os << *it;
  }
  return os << "]";
}
template <typename F, typename S>
ostream &operator<<(ostream &os, const map<F, S> &v) {
  os << "[";
  typename map<F, S>::const_iterator it;
  for (it = v.begin(); it != v.end(); it++) {
    if (it != v.begin()) os << ", ";
    os << it->first << " = " << it->second;
  }
  return os << "]";
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  ;
  int64_t t = 1;
  cin >> t;
  for (int64_t trr = 1; trr <= t; trr++) {
    int64_t n, p;
    cin >> n >> p;
    vector<pair<int64_t, int64_t> > vec;
    for (int64_t i = 1; i <= n; i++) {
      for (int64_t j = i + 1; j <= n; j++) {
        vec.push_back({i, j});
      }
    }
    for (int64_t i = 0; i < 2 * n + p; i++) {
      cout << vec[i].first << " " << vec[i].second << endl;
    }
  }
}

```