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;
template <class T, class U>
bool cmp_second(const pair<T, U> &a, const pair<T, U> &b) {
  return a.second < b.second;
}
pair<int, int> operator+(const pair<int, int> &a, const pair<int, int> &b) {
  return make_pair(a.first + b.first, a.second + b.second);
}
pair<int, int> operator-(const pair<int, int> &a, const pair<int, int> &b) {
  return make_pair(a.first - b.first, a.second - b.second);
}
pair<int, int> &operator+=(pair<int, int> &a, const pair<int, int> &b) {
  a.first += b.first;
  a.second += b.second;
  return a;
}
pair<int, int> &operator-=(pair<int, int> &a, const pair<int, int> &b) {
  a.first -= b.first;
  a.second -= b.second;
  return a;
}
inline int sg(int x) { return x ? (x > 0 ? 1 : -1) : 0; }
int n, m;
bool solve() {
  if (n == 3) {
    if (m != 3) return 0;
    printf("0 0\n");
    printf("0 1\n");
    printf("1 0\n");
    return 1;
  }
  if (n == 4) {
    if (m != 3 && m != 4) return 0;
    if (m == 3) {
      printf("0 1\n");
      printf("1 0\n");
      printf("1 1\n");
      printf("2 2\n");
    } else {
      printf("0 0\n");
      printf("0 1\n");
      printf("1 0\n");
      printf("1 1\n");
    }
    return 1;
  }
  if (n == 5) {
    if (m != 4 && m != 5) return 0;
    if (m == 4) {
      printf("0 0\n");
      printf("0 4\n");
      printf("4 0\n");
      printf("4 4\n");
      printf("1 2\n");
    } else {
      printf("0 0\n");
      printf("0 4\n");
      printf("4 0\n");
      printf("4 4\n");
      printf("1 5\n");
    }
    return 1;
  }
  if (n == 6 && m == 3) return 0;
  if (m * 2 < n) {
    return 0;
  }
  int h1 = m, h2 = n - m;
  vector<pair<int, int> > pt;
  for (int i = 0; i < h1; i++) printf("%d %d\n", i + 1, (h1 - i) * (h1 - i));
  for (int i = 0; i < h2; i++)
    printf("%d %d\n", -(i + 1), -(h2 - i) * (h2 - i));
  return 1;
}
int main(void) {
  scanf("%d %d", &(n), &(m));
  if (!solve()) puts("-1");
  return 0;
}