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;
pair<int, int> rec[210];
int n, m;
int main() {
  cin >> n >> m;
  if (m == 3) {
    if (n == 3) {
      puts("0 0\n10 0\n0 10");
    } else if (n == 4) {
      puts("0 0\n10 0\n0 10\n1 1");
    } else
      puts("-1");
    return 0;
  }
  int x = 0, y = 0;
  for (int i = 0; i < m; i++)
    rec[i] = pair<int, int>(x, y), x += 100000, y += (i + 1) * 100;
  for (int i = m; i < n; i++) {
    rec[i] = pair<int, int>(rec[i - m].first + 1, rec[i - m].second);
    if (i == m) rec[i] = pair<int, int>(-100000, -101);
    if (i - m == m - 1)
      rec[i] = pair<int, int>(100000000, rec[i - m].second + 1);
  }
  for (int i = 0; i < n; i++) printf("%d %d\n", rec[i].first, rec[i].second);
  return 0;
}