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.math.BigInteger;
import java.util.*;

public class Test {
    public static void main(String[] args) throws NumberFormatException,
            IOException {
        BufferedReader rd = new BufferedReader(new InputStreamReader(System.in));
        
        StringTokenizer st = new StringTokenizer(rd.readLine());
        int n = Integer.parseInt(st.nextToken());
        int m = Integer.parseInt(st.nextToken());
        if (m==3){
            if (n==5 || n==6){
                System.out.println(-1);
            }
            if (n==4){
                System.out.println("0 0");
                System.out.println("3 0");
                System.out.println("0 3");
                System.out.println("1 1");
            }
            if (n==3){
                System.out.println("0 0");
                System.out.println("1 0");
                System.out.println("0 1");
            }
        } else {
            for (int i=0; i<m; i++)
                System.out.println(i+" "+(sent+i*i));
            for (int i=0; i<n-m; i++)
                System.out.println(i+" "+(-sent-i*i));
        }
        System.out.flush();
    }
    private static final int sent = 10000000;
}