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;
bool InLine(pair<int, int> a, pair<int, int> b, pair<int, int> c) {
  return ((a.first * b.second + a.second * c.first + c.second * b.first -
           b.second * c.first - c.second * a.first - a.second * b.first) == 0);
}
int main() {
  ios_base::sync_with_stdio(0);
  int n, m;
  cin >> n >> m;
  if (m == 3) {
    if (n == 3)
      cout << "0 0\n3 0\n0 3";
    else if (n == 4)
      cout << "0 0\n3 0\n0 3\n1 1";
    else
      cout << -1;
  } else if (m == 4 && n == 8)
    cout << "0 0\n4 0\n4 5\n0 5\n"
         << "1 1\n3 1\n3 2\n1 2";
  else {
    vector<pair<int, int> > T;
    for (int i = (0); i <= (m - 1); ++i) T.push_back(make_pair(i, i * i));
    int ay = 2;
    for (int i = (1); i <= ((((n - m) < (m - 2)) ? (n - m) : (m - 2))); ++i) {
      int ax = (i + m + 1);
      bool lies = 1;
      while (lies) {
        ay++;
        lies = 0;
        for (int j = (0); j <= ((int)(T).size() - 1); ++j)
          for (int k = (j + 1); k <= ((int)(T).size() - 1); ++k)
            if (InLine(T[j], T[k], make_pair(ax, ay))) lies = 1;
      }
      T.push_back(make_pair(ax, ay));
    }
    for (int i = (0); i <= ((int)(T).size() - 1); ++i)
      cout << T[i].first << ' ' << T[i].second << '\n';
    if (m - 2 < n - m)
      for (int i = (1); i <= (n - 2 * m + 2); ++i)
        cout << (10000000 + i) << ' ' << 2 << '\n';
  }
  return 0;
}