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;
  scanf("%d%d", &n, &m);
  if (n >= 5 && m == 3) {
    return 0 * printf("-1\n");
  }
  vector<pair<int, int>> v;
  int pre = 0;
  int cur = 1000000;
  int MX = 500;
  for (int i = 1; i <= m; i++) {
    v.push_back({pre + MX - i, cur++});
    pre = pre + MX - i;
  }
  cur = -1000000;
  pre = 0;
  for (int i = 1; i <= n - m; i++) {
    v.push_back({pre + MX - i, cur--});
    pre = pre + MX - i;
  }
  for (auto t : v) {
    printf("%d %d\n", t.first, t.second);
  }
}