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.awt.geom.*;
import java.io.*;
import java.math.*;
import java.util.*;
import java.util.regex.*;
import static java.lang.Math.*;
public class B {

    void print(int x, int y) {
        buf.append(x).append(' ').append(y).append('\n');
    }

    public B() throws Exception {
        int n = in.nextInt();
        int m = in.nextInt();

        if (m==3 && n>=5) {
            System.out.println(-1);
            return;
        }

        for (int x=0; x<m; x++) print(x, x*x);
        for (int x=0; x<n-m; x++) print(x, -x*x-(1<<20));

        System.out.print(buf);
    }

    Scanner in = new Scanner(System.in);
    StringBuilder buf = new StringBuilder();
    public static void main(String[] args) throws Exception { // {{{
        new B();
    } // }}}
    public static void debug(Object... arr) { // {{{
        System.err.println(Arrays.deepToString(arr));
    } // }}}
}