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 java.io.*;
public class SetOfPoints
{
	public static void main(String[] args)
	{
		Scanner in = new Scanner(System.in);
		
		int n = in.nextInt();
		int m = in.nextInt();
		
		if(m == 3 && n > 4)
		{
			System.out.println("-1");
		}
		else
		{
			int y = 0;
			for(int x = 0; x < m; x++)
			{
				System.out.println((100 * x + 1000) + " " + y);
				y += (100 - x);
			}
			
			int a = 0;
			for(int b = 0; b < n - m; b++)
			{
				System.out.println(a + " " + (100 * b + 1000));
				a += (100 - b);
			}
		}
	}
}