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;
long long vp(pair<int, int> a, pair<int, int> b) {
  return (long long)a.first * b.second - (long long)a.second * b.first;
}
pair<int, int> mn(pair<int, int> a, pair<int, int> b) {
  return make_pair(a.first - b.first, a.second - b.second);
}
int main() {
  srand(239);
  int n, m;
  scanf("%d %d", &n, &m);
  if (m == 3) {
    if (n > 4) {
      printf("-1\n");
      return 0;
    }
    if (n == 3) {
      printf("0 0\n0 1\n1 0\n");
      return 0;
    }
    if (n == 4) {
      printf("0 0\n0 3\n3 0\n1 1\n");
      return 0;
    }
    assert(false);
  }
  int R1 = 1e7;
  int R2 = 2e7;
  vector<pair<int, int> > v;
  for (int i = 0; i < m; i++) {
    v.push_back(
        make_pair(R1 * cos(M_PI * 2 * i / m), R1 * sin(M_PI * 2 * i / m)));
    if (i < n - m)
      v.push_back(make_pair(R2 * cos(M_PI * 2 * i / m + M_PI * 0.0001),
                            R2 * sin(M_PI * 2 * i / m + M_PI * 0.0001)));
  }
  while (1) {
    bool good = true;
    for (int i = 0; i < n; i++) {
      for (int j = i + 1; j < n; j++) {
        for (int k = j + 1; k < n; k++) {
          if (vp(mn(v[i], v[k]), mn(v[j], v[k])) == 0) {
            v[k].first += rand() % 10;
            v[k].second += rand() % 10;
            good = false;
          }
        }
      }
    }
    if (good) break;
  }
  assert((int)(v).size() == n);
  for (int i = 0; i < n; i++) {
    printf("%d %d\n", v[i].first, v[i].second);
  }
  return 0;
}