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 int N = 105;
const double pi = acos(-1.0);
int X1[N], Y1[N], X2[N], Y2[N];
int main() {
  int n, m, i;
  scanf("%d%d", &n, &m);
  if (m == 3 && n > 4) {
    puts("-1");
    return 0;
  }
  if (m == 4 && n > 6) {
    if (n == 7) {
      puts("-10000000 10000000");
      puts("-10000000 -10000000");
      puts("10000000 10000000");
      puts("10000000 -10000000");
      puts("-500000 1000000");
      puts("500000 1000000");
      puts("500000 -1000000");
    } else if (n == 8) {
      puts("-10000000 10000000");
      puts("-10000000 -10000000");
      puts("10000000 10000000");
      puts("10000000 -10000000");
      puts("-500000 1000000");
      puts("500000 1000000");
      puts("-500000 -1000000");
      puts("500000 -1000000");
    }
    return 0;
  }
  int d = m / 2 * 2 + 1;
  for (i = 0; i < d; i++) {
    X1[i] = 10000000 * cos((double)i / d * 2 * pi) + 1;
    Y1[i] = 10000000 * sin((double)i / d * 2 * pi) + 1;
    X2[i] = 5000000 * cos((double)i / d * 2 * pi) - 1;
    Y2[i] = 5000000 * sin((double)i / d * 2 * pi) - 1;
  }
  for (i = 0; i < m; i++) printf("%d %d\n", X1[i], Y1[i]);
  for (i = 0; i < n - m; i++) printf("%d %d\n", X2[i], Y2[i]);
  return 0;
}