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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
long double R = 1e7;
long double pi = 3.1415;
long double pr = 0.000001;
long double ep = pr;
int n, m;
int main() {
  scanf("%d%d", &n, &m);
  if (m == 3 && (n == 6 || n == 5)) {
    printf("-1\n");
    return 0;
  }
  while (n > 0) {
    for (int i = 0; i < min(n, m); i++) {
      printf("%d %d\n", (int)(R * cos((i * 2 * pi + pr) / m)),
             (int)(R * sin((i * 2 * pi + pr) / m)));
    }
    n -= m;
    R -= 1000;
    pr += ep;
  }
  return 0;
}