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>
int main() {
  int i, n, m, ary[5][2] = {{0, 100}, {0, 0}, {100, 0}, {1, 1}, {1, 2}};
  scanf("%d%d", &n, &m);
  if (m == 3) {
    if (n >= 5) {
      puts("-1");
    } else {
      for (m = 0; m < n; m++) printf("%d %d\n", ary[m][0], ary[m][1]);
    }
    return 0;
  }
  int X = 10000;
  for (i = 0; i < m; i++) printf("%d %d\n", i, i * i + X);
  for (i = 0; i < n - m; i++) printf("%d %d\n", i, -X - i * i);
}