#include <bits/stdc++.h>
using ll = long long;
template <class ty>
void read(ty& a) {
  a = 0;
  int f = 0, c = getchar();
  for (; !isdigit(c); c = getchar()) f |= c == '-';
  for (; isdigit(c); c = getchar()) a = a * 10 + (c ^ 48);
  if (f) a = -a;
}
template <class A, class... B>
void read(A& a, B&... b) {
  read(a);
  read(b...);
}
using namespace std;
const int maxn = 26;
int a[maxn][maxn] = {};
void solve() {
  int n, p;
  read(n, p);
  memset(a, 0, sizeof a);
  for (int i = 0; i < 5; i++)
    for (int j = 0; j < 5; j++) a[i][j] = 1;
  for (int i = 5; i < n; i++) a[0][i] = a[1][i] = 1;
  for (int i = 0; i < n; i++)
    for (int j = i + 1; j < n; j++)
      if (p && a[i][j] == 0) p--, a[i][j] = 1;
  for (int i = 0; i < n; i++)
    for (int j = i + 1; j < n; j++)
      if (a[i][j]) printf("%d %d\n", i + 1, j + 1);
}
int main() {
  int t;
  read(t);
  while (t--) solve();
}

### Prompt

Generate 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 ll = long long;
template <class ty>
void read(ty& a) {
  a = 0;
  int f = 0, c = getchar();
  for (; !isdigit(c); c = getchar()) f |= c == '-';
  for (; isdigit(c); c = getchar()) a = a * 10 + (c ^ 48);
  if (f) a = -a;
}
template <class A, class... B>
void read(A& a, B&... b) {
  read(a);
  read(b...);
}
using namespace std;
const int maxn = 26;
int a[maxn][maxn] = {};
void solve() {
  int n, p;
  read(n, p);
  memset(a, 0, sizeof a);
  for (int i = 0; i < 5; i++)
    for (int j = 0; j < 5; j++) a[i][j] = 1;
  for (int i = 5; i < n; i++) a[0][i] = a[1][i] = 1;
  for (int i = 0; i < n; i++)
    for (int j = i + 1; j < n; j++)
      if (p && a[i][j] == 0) p--, a[i][j] = 1;
  for (int i = 0; i < n; i++)
    for (int j = i + 1; j < n; j++)
      if (a[i][j]) printf("%d %d\n", i + 1, j + 1);
}
int main() {
  int t;
  read(t);
  while (t--) solve();
}

```