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;
int t, n, m, k;
bool mark[30][30];
int main() {
  cin >> t;
  for (int qw = 0; qw < t; qw++) {
    memset(mark, false, sizeof mark);
    cin >> n >> m;
    k = n;
    while (k - 5 >= 5) {
      for (int i = k - 4; i <= k; i++)
        for (int j = i + 1; j <= k; j++) {
          mark[i][j] = true;
          mark[j][i] = true;
        }
      k -= 5;
    }
    if (k == 5) {
      for (int i = k - 4; i <= k; i++)
        for (int j = i + 1; j <= k; j++) {
          mark[i][j] = true;
          mark[j][i] = true;
        }
    }
    if (k == 6) {
      for (int i = k - 5; i <= k; i++)
        for (int j = i + 1; j <= k; j++) {
          mark[i][j] = true;
          mark[j][i] = true;
        }
      mark[1][2] = false;
      mark[2][1] = false;
      mark[3][4] = false;
      mark[4][3] = false;
      mark[5][6] = false;
      mark[6][5] = false;
    }
    if (k == 7) {
      for (int i = 1; i <= 3; i++)
        for (int j = 4; j <= 7; j++) {
          mark[i][j] = true;
          mark[j][i] = true;
        }
      mark[7][4] = true;
      mark[4][7] = true;
      mark[5][6] = true;
      mark[6][5] = true;
    }
    if (k == 8) {
      for (int i = 1; i <= 4; i++)
        for (int j = 5; j <= 8; j++) {
          mark[i][j] = true;
          mark[j][i] = true;
        }
    }
    if (k == 9) {
      for (int i = 1; i <= 3; i++)
        for (int j = 2; j <= 3; j++) {
          mark[i][j] = true;
          mark[j][i] = true;
        }
      for (int i = 4; i <= 6; i++)
        for (int j = 5; j <= 6; j++) {
          mark[i][j] = true;
          mark[j][i] = true;
        }
      for (int i = 7; i <= 9; i++)
        for (int j = 8; j <= 9; j++) {
          mark[i][j] = true;
          mark[j][i] = true;
        }
      k = 1;
      for (int i = 0; i < 3; i++)
        for (int j = 1; j < 3; j++) {
          mark[i * 3 + k][j * 3 + k] = true;
          mark[j * 3 + k][i * 3 + k] = true;
        }
      k = 2;
      for (int i = 0; i < 3; i++)
        for (int j = 1; j < 3; j++) {
          mark[i * 3 + k][j * 3 + k] = true;
          mark[j * 3 + k][i * 3 + k] = true;
        }
      k = 3;
      for (int i = 0; i < 3; i++)
        for (int j = 1; j < 3; j++) {
          mark[i * 3 + k][j * 3 + k] = true;
          mark[j * 3 + k][i * 3 + k] = true;
        }
    }
    for (int i = 1; i <= n; i++)
      for (int j = i + 1; j <= n; j++) {
        if (mark[i][j]) {
          cout << i << " " << j << endl;
          continue;
        }
        if (m > 0) {
          cout << i << " " << j << endl;
          m--;
        }
      }
  }
}
