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;
int n, m;
int main() {
  scanf("%d%d", &n, &m);
  if (m == 3 && n >= 5) {
    printf("-1\n");
    return 0;
  }
  for (int i = 0; i < m; ++i) {
    double x, y;
    x = 99999999 *
        cos((double)i * 3.1415926535897932384626433832795 * 2 / (double)m);
    y = 99999999 *
        sin((double)i * 3.1415926535897932384626433832795 * 2 / (double)m);
    int xx = (int)x, yy = (int)y;
    printf("%d %d\n", xx, yy);
  }
  for (int i = 0; i < n - m; ++i) {
    double x, y;
    x = 1000000 *
        cos((double)i * 3.1415926535897932384626433832795 * 2 / (double)m +
            1e-5);
    y = 1000000 *
        sin((double)i * 3.1415926535897932384626433832795 * 2 / (double)m +
            1e-5);
    int xx = (int)x, yy = (int)y;
    x = 99999999 *
        cos((double)i * 3.1415926535897932384626433832795 * 2 / (double)m);
    y = 99999999 *
        sin((double)i * 3.1415926535897932384626433832795 * 2 / (double)m);
    int xxx = (int)x, yyy = (int)y;
    if ((long long)xx * (long long)yyy == (long long)yy * (long long)xxx) yy++;
    printf("%d %d\n", xx, yy);
  }
}