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 n, m;
vector<pair<int, int> > p;
bool ok(int x, int y) {
  int sz = p.size();
  if (sz < 2) return true;
  for (int i = 0; i < sz; i++)
    for (int j = i + 1; j < sz; j++) {
      if ((p[i].first - x) * (p[j].second - y) ==
          (p[j].first - x) * (p[i].second - y))
        return false;
    }
  return true;
}
int main() {
  scanf("%d%d", &n, &m);
  if (m == 3) {
    if (n > 4)
      puts("-1");
    else {
      puts("0 0\n3 0\n0 3");
      if (n == 4) puts("1 1");
    }
    return 0;
  }
  int cnt1 = 0;
  int cnt2 = 0;
  for (int i = -999; cnt1 < m; i += 2) {
    if (ok(i, i * i)) {
      cnt1++;
      p.push_back(make_pair(i, i * i));
      if (cnt2 < n - m) {
        cnt2++;
        p.push_back(make_pair(i, -i * i));
      }
    }
  }
  for (int i = 0; i < n; i++) printf("%d %d\n", p[i].first, p[i].second);
  return 0;
}