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 == 3) {
    printf("0 0\n1 0\n0 1\n");
    return 0;
  }
  if (m == 3) {
    if (n == 4)
      printf("0 0\n4 0\n0 4\n1 1\n");
    else
      printf("-1\n");
    return 0;
  }
  int i;
  vector<pair<int, int> > v;
  if (m == 4) {
    v.push_back(pair<int, int>(0, 0));
    v.push_back(pair<int, int>(9, 0));
    v.push_back(pair<int, int>(0, 9));
    v.push_back(pair<int, int>(9, 9));
    v.push_back(pair<int, int>(4, 1));
    v.push_back(pair<int, int>(4, 8));
    v.push_back(pair<int, int>(5, 1));
    v.push_back(pair<int, int>(5, 8));
    for (i = (0); i < (n); ++i) printf("%d %d\n", v[i].first, v[i].second);
    return 0;
  }
  int r = 1 << 20;
  int z = m;
  if (z % 2 == 0) ++z;
  for (i = (0); i < (m); ++i) {
    double alpha = i * (4 * acos(0.0) / z);
    int x = int(r * cos(alpha));
    int y = int(r * sin(alpha));
    v.push_back(pair<int, int>(x, y));
    if (i < n - m) v.push_back(pair<int, int>(x + x, y + y));
  }
  for (i = (0); i < (n); ++i) printf("%d %d\n", v[i].first, v[i].second);
  return 0;
};