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.*;
import java.math.*;
public class Main {
static long radius=99999999;
static long radius2=99999;
public static void main(String[] args)throws IOException{
Scanner sc=new Scanner(System.in);
PrintWriter pw=new PrintWriter((System.out));

int n,m;
n=sc.nextInt();
m=sc.nextInt();
if(m==3 && n>=5){
System.out.print(-1);
}else{
Double alpha=Math.PI*2/m;
for(int i=0;i<m;i++){
System.out.print(Math.round(radius*Math.cos(alpha*i)));
System.out.print(" ");
System.out.println(Math.round(radius*Math.sin(alpha*i)));

}
if(n-m>0){
alpha=Math.PI*2/(n-m);
double dalpha=Math.PI*2/3000;
for (int i=0;i<n-m;i++){
System.out.print(Math.round(radius2*Math.cos(alpha*i+dalpha)));
System.out.print(" ");
System.out.println(Math.round(radius2*Math.sin(alpha*i+dalpha)));

}
}
}
}
}