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;
struct classcomp {
  bool operator()(const int& lhs, const int& rhs) const { return lhs < rhs; }
};
int main() {
  int n, m;
  cin >> n >> m;
  if (m == 3) {
    if (n >= 5) {
      cout << "-1" << endl;
      return 0;
    }
    if (n == 4) {
      cout << "0 0" << endl;
      cout << "3 0" << endl;
      cout << "0 3" << endl;
      cout << "1 1" << endl;
      return 0;
    } else {
      cout << "0 0" << endl;
      cout << "3 0" << endl;
      cout << "0 3" << endl;
      return 0;
    }
  }
  int j = 0;
  double r = 10000000;
  double x = 0, y = 0;
  while (true) {
    for (int i = 0; i < m; i++, j++) {
      if (j >= n) return 0;
      printf(
          "%d %d\n",
          (int)(r * cos(2 * 3.1415926535897932384626433832795 * (i + x) / m)),
          (int)(r * sin(2 * 3.1415926535897932384626433832795 * (x + i) / m)));
    }
    r = r - 90000;
    x += 0.000010;
  }
  return 0;
}