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.*;
import java.util.*;

public class B implements Runnable {

	private void Solution() throws IOException {
		int n = nextInt(), m = nextInt();
		if (m == 3) {
			if (n == 3) {
				println(0, 0);
				println(1, 2);
				println(2, 0);
			} else if (n == 4) {
				println(-4, 0);
				println(4, 0);
				println(0, 6);
				println(0, 1);
			} else {
				print(-1);
			}
			return;
		}
		int x = 10000000, y = 0;
		double angle = 2 * Math.PI / m;
		for (int i = 0; i < m; i++) {
			println(x, y);
			int nx = (int) (x * Math.cos(angle) - y * Math.sin(angle));
			int ny = (int) (x * Math.sin(angle) + y * Math.cos(angle));
			x = nx;
			y = ny;
		}
		if (m == n)
			return;
		angle = 2 * Math.PI / (n - m);
		x = 43676;
		y = 89543;
		for (int i = 0; i < n - m; i++) {
			println(x, y);
			int nx = (int) (x * Math.cos(angle) - y * Math.sin(angle));
			int ny = (int) (x * Math.sin(angle) + y * Math.cos(angle));
			x = nx;
			y = ny;
		}
	}

	public static void main(String[] args) {
		new B().run();
	}

	BufferedReader in;
	PrintWriter out;
	StringTokenizer tokenizer;

	public void run() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
			Solution();
			out.close();
		} catch (Exception e) {
			e.printStackTrace();
			System.exit(261);
		}
	}

	void halt() {
		out.close();
		System.exit(0);
	}

	void print(Object... obj) {
		for (int i = 0; i < obj.length; i++) {
			if (i != 0)
				out.print(" ");
			out.print(obj[i]);
		}
	}

	void println(Object... obj) {
		print(obj);
		out.println();
	}

	int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	long nextLong() throws NumberFormatException, IOException {
		return Long.parseLong(nextToken());
	}

	double nextDouble() throws NumberFormatException, IOException {
		return Double.parseDouble(nextToken());
	}

	String nextLine() throws IOException {
		return in.readLine();
	}

	String nextToken() throws IOException {
		while (tokenizer == null || !tokenizer.hasMoreTokens())
			tokenizer = new StringTokenizer(nextLine());
		return tokenizer.nextToken();
	}
}