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;
bool debug = false;
int n, m, k;
int dx[4] = {0, 1, 0, -1}, dy[4] = {1, 0, -1, 0};
long long ln, lk, lm;
int main() {
  scanf("%d%d", &n, &m);
  if (m == 3) {
    if (n == 3)
      printf("%d %d\n%d %d\n%d %d\n", 0, 0, 0, 1, 1, 1);
    else if (n == 4) {
      printf("%d %d\n%d %d\n%d %d\n%d %d\n", 0, 0, 1, 1, 1, 2, 2, 1);
    } else
      puts("-1");
    return 0;
  }
  int y = 1e7;
  for (int(i) = 1; (i) <= (int)(m); (i)++) printf("%d %d\n", i, i * i + y);
  for (int(i) = 1; (i) <= (int)(n - m); (i)++) printf("%d %d\n", i, -i * i - y);
  return 0;
}