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 main() {
  int n, m;
  cin >> n >> m;
  double a;
  int x, y;
  a = (2 * acos(-1)) / m;
  if (m == 3 && n >= 5) {
    cout << "-1\n";
    return 0;
  }
  for (int i = 0; i < m; i++) {
    x = 100000000 * cos(a * i) / 2;
    y = 100000000 * sin(a * i) / 2;
    cout << x << " " << y << endl;
  }
  for (double i = 0; i < (n - m); i++) {
    x = (100000000) * cos(a * i + 0.00000005);
    y = (100000000) * sin(a * i + 0.00000005);
    cout << x << " " << y << endl;
  }
}