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>
const double lp = 20000000;
const int maxn = 250;
const double PI = atan2(0, -1);
int n, m;
int xa[maxn], ya[maxn], xb[maxn], yb[maxn];
int main() {
  scanf("%d%d", &n, &m);
  if (m == 3) {
    if (n > 4) {
      printf("-1\n");
      return 0;
    }
    printf("0 1\n1 -1\n-1 -1\n");
    if (n == 4) printf("0 0\n");
    return 0;
  }
  if (m == 4 && n == 7) {
    printf(
        "176166 6377\n"
        "709276 539564\n"
        "654734 174109\n"
        "910147 434207\n"
        "790497 366519\n"
        "606663 21061\n"
        "859328 886001\n");
    return 0;
  }
  if (m == 4 && n == 8) {
    printf("0 0\n1 1\n3 1\n4 0\n0 3\n1 2\n3 2\n4 3\n");
    return 0;
  }
  int t = m & 1 ? m : m + 1;
  for (int i = 0; i < t; ++i) {
    xa[i] = 0.7 * static_cast<int>(lp * cos(static_cast<double>(i) * 2.0 * PI /
                                            static_cast<double>(t)));
    ya[i] = 0.7 * static_cast<int>(lp * sin(static_cast<double>(i) * 2.0 * PI /
                                            static_cast<double>(t)));
    xb[i] = 4 * xa[i];
    yb[i] = 4 * ya[i];
  }
  for (int i = 0; i < m; ++i) printf("%d %d\n", xb[i], yb[i]);
  for (int i = 0; i < n - m; ++i) printf("%d %d\n", xa[i], ya[i]);
  return 0;
}