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 sh(int x, int it, int tp) {
  if (m % 2 == 0 && tp == 1) {
    return -1 - tp - x - rand() % (5 + 5 * tp);
  }
  return 0;
}
int main() {
  const double pi = acos(-1.);
  cin >> n >> m;
  if (m == 3 && n > 4) {
    puts("-1");
    return 0;
  }
  int nm = n - m;
  for (int i = (0); i < (m); i++) {
    double dx = cos(2 * pi * i / m);
    double dy = sin(2 * pi * i / m);
    cout << int(dx * 10000000) + sh(0, i, 0) << ' '
         << int(dy * 10000000) + sh(1, i, 0) << endl;
    if (nm) {
      cout << int(dx * 10000) + sh(0, i, 1) << ' '
           << int(dy * 10000) + sh(1, i, 1) << endl;
      nm--;
    }
  }
  return 0;
}