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;
const int maxint = -1u >> 1;
template <class T>
bool get_max(T& a, const T& b) {
  return b > a ? a = b, 1 : 0;
}
template <class T>
bool get_min(T& a, const T& b) {
  return b < a ? a = b, 1 : 0;
}
const double pi = acos(-1.0);
int n, m;
void build(int n, double r, double base) {
  double arg = 2.0 * pi / n;
  for (int i = 0; i < n; i++) {
    int x = r * cos(i * arg + base);
    int y = r * sin(i * arg + base);
    printf("%d %d\n", x, y);
  }
}
int main() {
  scanf("%d%d", &n, &m);
  if (n >= 5 && m == 3)
    printf("-1\n");
  else {
    build(m, 1e8, 0.0);
    build(n - m, 1e3, 27);
  }
  return 0;
}