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.io.BufferedReader;
import java.io.InputStreamReader;

public class A {

	public static void main(String[] args) throws Exception {
		A main = new A();
		main.run();
		System.exit(0);
	}

	private void run() throws Exception {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		String[] strs = in.readLine().split("\\s");
		int n = Integer.parseInt(strs[0]);
		int m = Integer.parseInt(strs[1]);
		if (n - m >= 2 && m < 4) {
			System.out.println(-1);
			return;
		}

		for (int i = 1; i <= m; i++) {
			System.out.println(String.format("%d %d", i, i * (i + 1) / 2));
		}
		for (int i = 1; i <= n - m; i++) {
			System.out.println(String.format("%d %d", 100000 + i * (i + 1) / 2,
					i));
		}
	}
}