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, m;
int main() {
  scanf("%d%d", &n, &m);
  int k = 17;
  if (m == 3 && n - m >= 2) {
    printf("-1\n");
    return 0;
  }
  if (m & 1) {
    printf("0 0\n");
    for (int i = 1; i <= m / 2; i++)
      printf("%d %d\n", i, i * i), printf("%d %d\n", -i, i * i);
  } else {
    for (int i = 1; i <= m / 2; i++)
      printf("%d %d\n", i, k * i * i), printf("%d %d\n", -i, k * i * i);
  }
  int b = -10086, k1 = -13, k2 = -13;
  for (int i = 1; i <= (n - m) / 2; i++) {
    printf("%d %d\n", i, k2 * i * i + b), printf("%d %d\n", -i, k2 * i * i + b);
  }
  if ((n - m) & 1) {
    printf("%d %d\n", ((n - m) / 2 + 1),
           k1 * ((n - m) / 2 + 1) * ((n - m) / 2 + 1) + b);
  }
}