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;
  while (scanf("%d%d", &n, &m) >= 1) {
    if (m == 3) {
      switch (n) {
        case 3:
          printf("0 0\n3 0\n0 3\n");
          break;
        case 4:
          printf("0 0\n3 0\n0 3\n1 1\n");
          break;
        case 5:
        case 6:
          printf("-1\n");
          break;
      }
      continue;
    }
    vector<pair<int, int> > pts(m);
    int mid = m / 2;
    int dn = -1e9;
    for (int i = 0; i < m; i++) {
      pts[i] = make_pair(i, (i - mid) * (i - mid));
      dn = max(dn, pts[i].second);
    }
    const int MAXC = int(1e8);
    for (int i = 0; i < m; i++)
      printf("%d %d\n", pts[i].first, MAXC - dn + pts[i].second);
    for (int i = 0; i < n - m; i++)
      printf("%d %d\n", pts[i].first, -(MAXC - dn + pts[i].second));
  }
  return 0;
}