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>
#pragma comment(linker, "/STACK:32000000")
using namespace std;
const int MAXN = 59049;
bool g[55][55];
int deg[55];
void PutEdge(int n) {
  int besti = -1, bestj = -1;
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j < n; ++j) {
      if (i != j && deg[i] < n - 1 && deg[j] < n - 1) {
        if (!g[i][j]) {
          if (besti == -1 || deg[besti] >= deg[i]) {
            if (bestj == -1 || deg[bestj] > deg[j]) {
              besti = i;
              bestj = j;
            }
          }
        }
      }
    }
  }
  g[besti][bestj] = g[bestj][besti] = true;
  ++deg[besti];
  ++deg[bestj];
}
int main() {
  int test;
  scanf("%d", &test);
  while (test--) {
    memset((g), 0, sizeof(g));
    int n, p;
    cin >> n >> p;
    memset((deg), 0, sizeof(deg));
    for (int i = 0; i < 2 * n + p; ++i) {
      PutEdge(n);
    }
    for (int i = 0; i < n; ++i) {
      for (int j = i; j < n; ++j) {
        if (g[i][j]) {
          printf("%d %d\n", i + 1, j + 1);
        }
      }
    }
  }
  return 0;
}
