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 long long INF = 1e6;
long long n, m;
signed main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long T = 1;
  while (T--) {
    cin >> n >> m;
    if (m == 3) {
      if (n == 3)
        cout << "3 0\n0 0\n0 3\n";
      else if (n == 4)
        cout << "3 0\n0 0\n0 3\n1 1\n";
      else
        cout << "-1\n";
      return 0;
    }
    for (long long i = 0; i < m; i++) {
      long long j = i * i;
      cout << i << ' ' << j << '\n';
      if (i < n - m) cout << i << ' ' << -INF - j << '\n';
    }
  }
  return 0;
}