Problem: Convexity of a set of points on the plane is the size of the largest subset of points that form a convex polygon. Your task is to build a set of n points with the convexity of exactly m. Your set of points should not contain three points that lie on a straight line.

Input

The single line contains two integers n and m (3 ≤ m ≤ 100, m ≤ n ≤ 2m).

Output

If there is no solution, print "-1". Otherwise, print n pairs of integers — the coordinates of points of any set with the convexity of m. The coordinates shouldn't exceed 108 in their absolute value.

Examples

Input

4 3


Output

0 0
3 0
0 3
1 1


Input

6 3


Output

-1


Input

6 6


Output

10 0
-10 0
10 1
9 1
9 -1
0 -2


Input

7 4


Output

176166 6377
709276 539564
654734 174109
910147 434207
790497 366519
606663 21061
859328 886001

Solution (in JAVA):

Solution:
import java.util.*;

import static java.lang.System.*;

public class D278 {
    Scanner sc = new Scanner(in);
    public static Random rand=new Random();


    public void run() {
        int n=sc.nextInt();
        int m=sc.nextInt();
        if(m==3){
            switch(n){
            case 3:
                ln("0 0");
                ln("1 0");
                ln("0 1");
                return;
            case 4:
                ln("0 0");
                ln("0 3");
                ln("3 0");
                ln("1 1");
                return;
            default:
                ln(-1);
                return;
            }
        }

        for(int x=1;x<=n-m;x++){
            ln(x+" "+(10000000+x*x));
        }
        for(int x=1;x<=m;x++){
            ln(x+" "+(-10000000-x*x));
        }
    }

    public static void main(String[] _) {
        new D278().run();
    }


    public int[] nextIntArray(int n){
        int[] res=new int[n];
        for(int i=0;i<n;i++){
            res[i]=sc.nextInt();
        }
        return res;
    }
    public static void pr(Object o) {
        out.print(o);
    }
    public static void ln(Object o) {
        out.println(o);
    }
    public static void ln() {
        out.println();
    }
}