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
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class A {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] temp = br.readLine().split(" ");
        int tt = Integer.parseInt(temp[0]);
        StringBuilder sb = new StringBuilder();
        for (int ttt = 0; ttt < tt; ttt++) {
            temp = br.readLine().split(" ");
            int n = Integer.parseInt(temp[0]);
            boolean[][] x = new boolean[n + 1][n + 1];
            for (int i = 0; i <= n; i++) x[i][i] = true;
            int p = Integer.parseInt(temp[1]);
            for (int i = 1; i <= n; i++) {
                int a = i;
                int b = i + 1;
                int c = i + 2;
                if (b > n) b -= n;
                if (c > n) c -= n;
                sb.append(a);
                sb.append(' ');
                sb.append(b);
                sb.append('\n');
                sb.append(a);
                sb.append(' ');
                sb.append(c);
                sb.append('\n');
                x[a][b] = true;
                x[b][a] = true;
                x[a][c] = true;
                x[c][a] = true;
            }
            int k = 0;
            outer:
            for (int i = 1; i <= n && k < p; i++) {
                for (int j = 1; j <= n && k < p; j++) {
                    if (!x[i][j]) {
                        sb.append(i);
                        sb.append(' ');
                        sb.append(j);
                        sb.append('\n');
                        x[i][j] = true;
                        x[j][i] = true;
                        k++;
                    }

                }
            }
        }
        System.out.println(sb);
    }
}
