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
#include <bits/stdc++.h>
using namespace std;
template <class P, class Q>
void mmin(P &a, const Q &b) {
  if (b < a) a = b;
}
template <class P, class Q>
void mmax(P &a, const Q &b) {
  if (b > a) a = b;
}
template <class P, class Q>
bool mminb(P &a, const Q &b) {
  if (b < a) return a = b, true;
  return false;
}
template <class P, class Q>
bool mmaxb(P &a, const Q &b) {
  if (b > a) return a = b, true;
  return false;
}
template <class P>
P GCD(P a, P b) {
  if (a < b) swap(a, b);
  P c;
  while (b) {
    c = a % b;
    a = b;
    b = c;
  }
  return a;
}
const int MAXn = 24;
int n, p;
bool adj[MAXn][MAXn];
bool t[MAXn][MAXn];
int ar[24] = {1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 2, 3,
              2, 4, 2, 5, 2, 6, 3, 4, 3, 5, 3, 6};
int main() {
  ios_base::sync_with_stdio(false);
  for (int i = 0; i < (24); ++i) --ar[i];
  int t;
  cin >> t;
  while (t--) {
    cin >> n >> p;
    if (n != 6) {
      memset(adj, 0, sizeof(adj));
      int x = 2;
      while (GCD(n, x) != 1) ++x;
      for (int i = 0; i < (n); ++i) {
        adj[i][(i + 1) % n] = adj[(i + 1) % n][i] = true;
        adj[i][(i + x) % n] = adj[(i + x) % n][i] = true;
      }
    } else {
      for (int i = 0; i < (12); ++i)
        adj[ar[2 * i]][ar[2 * i + 1]] = adj[ar[2 * i + 1]][ar[2 * i]] = true;
    }
    for (int i = 0; i < n; ++i)
      for (int j = 0; j < n && p; ++j)
        if (i != j && !adj[i][j]) {
          --p;
          adj[i][j] = adj[j][i] = true;
        }
    for (int i = 0; i < (n); ++i)
      for (int j = 0; j < (i); ++j)
        if (adj[i][j]) cout << j + 1 << ' ' << i + 1 << endl;
  }
}
