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 double eps = 1e-9;
const int inf = (int)1e9;
const int maxn = (int)210;
int x[maxn], y[maxn];
double alp = 0.239;
int c = 0;
inline void add(double bet, double R) {
  bet += alp;
  double xx = R * cos(bet);
  double yy = R * sin(bet);
  x[c] = (int)floor(xx), y[c] = (int)floor(yy);
  c++;
}
int main() {
  int n, m;
  scanf("%d%d", &n, &m);
  if (m == 3 && n == 4) return 0 * printf("0 0\n0 3\n3 0\n1 1\n");
  if (m == 3 && n == 5) return 0 * printf("-1\n");
  if (m == 3 && n == 6) return 0 * printf("-1\n");
  for (int i = 0; (i) < (m); ++(i)) {
    add(i * 2 * acos(-1.) / m, 1e6);
    if (n - m > i) add(i * 2 * acos(-1.) / m, 1e6 - 10);
  }
  for (int i = 0; (i) < (n); ++(i)) printf("%d %d\n", x[i], y[i]);
  return 0;
}