#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 5, M = 3, nBits = 2e8 + 5, MM = (1 << 16), MAX = 1111,
          OO = 0x3f3f3f3f, MOD = 998244353, inf = 1 << 30;
const double PI = acos(-1);
const long long INF = (long long)1e18;
long long GCD(long long a, long long b) { return !b ? a : GCD(b, a % b); }
long long LCM(long long x, long long y) { return (x * y / GCD(x, y)); }
long long fact(long long z) { return (z <= 1) ? 1 : z * fact(z - 1); }
int X[] = {0, 0, 1, -1, 1, -1, 1, -1};
int Y[] = {1, -1, 0, 0, 1, -1, -1, 1};
int n, q, y, x, t;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> q;
  while (q--) {
    cin >> x >> y;
    t = 2 * x + y;
    for (int i = 1; i <= x && t; ++i)
      for (int j = i + 1; j <= x && t; ++j) cout << i << " " << j << endl, --t;
  }
  return 0;
}

### 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;
const int N = 2e5 + 5, M = 3, nBits = 2e8 + 5, MM = (1 << 16), MAX = 1111,
          OO = 0x3f3f3f3f, MOD = 998244353, inf = 1 << 30;
const double PI = acos(-1);
const long long INF = (long long)1e18;
long long GCD(long long a, long long b) { return !b ? a : GCD(b, a % b); }
long long LCM(long long x, long long y) { return (x * y / GCD(x, y)); }
long long fact(long long z) { return (z <= 1) ? 1 : z * fact(z - 1); }
int X[] = {0, 0, 1, -1, 1, -1, 1, -1};
int Y[] = {1, -1, 0, 0, 1, -1, -1, 1};
int n, q, y, x, t;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> q;
  while (q--) {
    cin >> x >> y;
    t = 2 * x + y;
    for (int i = 1; i <= x && t; ++i)
      for (int j = i + 1; j <= x && t; ++j) cout << i << " " << j << endl, --t;
  }
  return 0;
}

```