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;
int n, k, x, dy, y;
void p(int x, int y) { printf("%d %d\n", x, y); }
int main() {
  scanf("%d%d", &n, &k);
  if (k == 3) {
    if (n == 3) {
      printf("0 0\n0 1\n1 0\n");
      return 0;
    }
    if (n == 4) {
      printf("0 0\n0 100\n100 0\n1 1\n");
      return 0;
    }
    printf("-1");
    return 0;
  }
  p(0, 0);
  n--;
  k--;
  dy = 300;
  x = 0;
  y = 0;
  while (k > 0) {
    x--;
    dy--;
    p(x, y + dy);
    k--;
    n--;
    if (k == 0) break;
    p(x, -y - dy);
    k--;
    n--;
    y += dy;
  }
  dy = 300;
  x = 100;
  y = 0;
  while (n > 0) {
    x++;
    dy--;
    p(x, y + dy);
    n--;
    if (n == 0) break;
    p(x, -y - dy);
    n--;
    y += dy;
  }
  return 0;
}