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 bigmod(int b, int p, int m) {
  int res = 1, x = b;
  while (p) {
    if (p & 1) res = (res * x) % m;
    x = (x * x) % m;
    p >>= 1;
  }
  return res;
}
int ex_euc(int aa, int bb, int *xx, int *yy) {
  int x, y, u, v, m, n, a, b, q, r;
  x = 0, y = 1;
  u = 1, v = 0;
  for (a = aa, b = bb; a != 0; b = a, a = r, x = u, y = v, u = m, v = n) {
    q = b / a;
    r = b % a;
    m = x - (u * q);
    n = y - (v * q);
  }
  *xx = x;
  *yy = y;
  return b;
}
int gcd(int a, int b) {
  int c;
  while (b) {
    c = a % b;
    a = b;
    b = c;
  }
  return a;
}
int lcm(int a, int b) { return (int)(a * (b / gcd(a, b))); }
int Pow(int a, int p) {
  int res = 1, x = a;
  while (p) {
    if (p & 1) res = res * x;
    x = x * x;
    p >>= 1;
  }
  return res;
}
int Max(int a, int b) { return a > b ? a : b; }
int Min(int a, int b) { return a < b ? a : b; }
int Abs(int a) { return a < 0 ? -a : a; }
struct SM {
  int a, b;
};
bool cmp(SM a, SM b) { return a.a < b.a; }
int main() {
  int t, n, p, i, j, k;
  scanf("%d", &t);
  while (t--) {
    scanf("%d%d", &n, &p);
    k = 2 * n + p;
    for (i = 1; i <= n; i++) {
      for (j = i + 1; j <= n; j++) {
        if (k == 0) break;
        printf("%d %d\n", i, j);
        k--;
      }
      if (k == 0) break;
    }
  }
  return 0;
}
