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.IOException;
import java.io.PrintWriter;
import java.util.Scanner;

public class A {

    static void solve() throws IOException {
        int tn = in.nextInt();
        for ( ; tn > 0; tn -- ) {
            int n = in.nextInt();
            int p = in.nextInt();
            boolean[][] e = new boolean[n][n];
            for ( int i = 0; i < n; i ++ ) {
                for ( int j = i - 2; j <= i + 2; j ++ ) {
                    if ( j == i ) {
                        continue;
                    }
                    if ( j < 0 ) {
                        e[i][j + n] = true;
                        e[j + n][i] = true;
                    } else if ( j >= n ) {
                        e[i][j - n] = true;
                        e[j - n][i] = true;
                    } else {
                        e[i][j] = true;
                        e[j][i] = true;
                    }
                }
            }
            for ( int i = 0; i < n; i ++ ) {
                for ( int j = i + 1; j < n; j ++ ) {
                    if ( p > 0 && ! e[i][j] ) {
                        e[i][j] = true;
                        e[j][i] = true;
                        p --;
                    }
                }
            }
            while ( p != 0 ) {
                p = p;
            }
            for ( int i = 0; i < n; i ++ ) {
                for ( int j = i + 1; j < n; j ++ ) {
                    if ( e[i][j] ) {
                        out.println( ( i + 1 ) + " " + ( j + 1 ) );
                    }
                }
            }
        }
    }

    static Scanner in;
//    static StreamTokenizer in;
    static PrintWriter out;

//    static int nextInt() throws IOException {
//        in.nextToken();
//        return ( int ) in.nval;
//    }

    public static void main( String[] args ) throws IOException {
        in = new Scanner( System.in );
//        in = new StreamTokenizer( new InputStreamReader( System.in ) );
        out = new PrintWriter( System.out );
        solve();
        out.close();
    }
}
