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;
const double PI = 3.14159265358979;
int n, m;
int main() {
  cin >> n >> m;
  if (m == 3) {
    if (n == 3)
      cout << "0 0\n1 0\n0 1\n";
    else if (n == 4)
      cout << "0 0\n3 0\n0 3\n1 1\n";
    else
      cout << "-1\n";
    return 0;
  }
  if (n > 6 && m == 4) {
    cout << "176166 6377\n709276 539564\n654734 174109\n910147 434207\n790497 "
            "366519\n606663 21061\n859328 886001\n";
    if (n == 8) cout << "452078 233304";
    return 0;
  }
  for (int i = 0; i < m; i++) {
    cout << 2 * (int)(10000000 * cos(2 * PI / m * i) + i * i) << " "
         << 2 * (int)(10000000 * sin(2 * PI / m * i) + (i + 1) * i) << '\n';
    if (n - m > i)
      cout << (int)(10000000 * cos(2 * PI / m * i) + i * i) << " "
           << (int)(10000000 * sin(2 * PI / m * i) + (i + 1) * i) << '\n';
  }
}