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.*;

public class B {
	private static Scanner in;

	public void run() {
		int n = in.nextInt();
		int m = in.nextInt();
		if (m == 3) {
			if (n == 3) {
				System.out.println("0 0\n0 3\n3 0");
				return;
			}
			if (n == 4) {
				System.out.println("0 0\n0 3\n3 0\n1 1");
				return;
			}
			System.out.println(-1);
			return;
		}
		for (int i = 0; i < n; i++) {
			double ang = 2 * Math.PI * i / m;
			double r = 100000000;
			if (i >= m) {
				r *= 0.999;
				ang += 0.0000001;
			}
			System.out.println(Math.round(r * Math.cos(ang)) + " " + Math.round(r * Math.sin(ang)));
		}
	}

	public static void main(String[] args) {
		Locale.setDefault(Locale.US);
		in = new Scanner(System.in);
		new B().run();
		in.close();
	}
}