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 pi = acos(-1);
int main() {
  int N, M;
  srand(time(0));
  cin >> N >> M;
  if (M == 3 && N >= 5)
    cout << -1 << endl;
  else {
    double a = 2 * pi / M;
    for (int i = 1; i <= M; i++) {
      printf("%d %d\n", (int)(1e8 / 2 * cos(a * i)) + rand() % 2000 - 1000,
             (int)(1e8 / 2 * sin(a * i)) + rand() % 2000 - 1000);
    }
    for (int i = M + 1; i <= N; i++) {
      printf("%d %d\n", (int)(1e7 * cos(a * i)) + rand() % 2000 - 1000,
             (int)(1e7 * sin(a * i)) + rand() % 2000 - 1000);
    }
  }
}