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>
double PI;
void init() { PI = acos(-1); }
int main() {
  int n, m;
  init();
  scanf("%d%d", &n, &m);
  if (m == 3) {
    if (n >= 5) {
      printf("-1\n");
      return 0;
    }
    printf("0 0\n");
    printf("0 3\n");
    printf("3 0\n");
    if (n == 4) printf("1 1\n");
  } else if (m == 4) {
    printf("10 10\n");
    printf("0 0\n");
    printf("0 10\n");
    printf("10 0\n");
    if (n >= 5) printf("12 13\n");
    if (n >= 6) printf("-2 -3\n");
    if (n >= 7) printf("-3 12\n");
    if (n >= 8) printf("13 -2\n");
  } else {
    int k = m % 2 == 0 ? m + 1 : m;
    int i;
    for (i = 0; i < n; i++) {
      double r, a;
      int j, x, y;
      r = i < m ? 8e7 : 9e7;
      j = i % m;
      a = PI * 2 * j / k;
      x = round(r * cos(a));
      y = round(r * sin(a));
      printf("%d %d\n", x, y);
    }
  }
  return 0;
}