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 tau = 2 * acos(-1);
const int R = 9e7;
int main() {
  srand(time(0));
  int n, m;
  cin >> n >> m;
  if (m == 3) {
    if (n == 3 || n == 4) cout << "0 0\n3 0\n0 3\n";
    if (n == 4) cout << "1 1\n";
    if (n >= 5) {
      cout << "-1" << endl;
      return 0;
    }
    return 0;
  }
  if (m == 4) {
    cout << "0 0\n7 0\n5 2\n2 3\n";
    if (n >= 5) cout << "2 7\n";
    if (n >= 6) cout << "6 3\n";
    if (n >= 7) cout << "15 -1\n";
    if (n >= 8) cout << "-1 -1\n";
    return 0;
  }
  int rr = rand();
  for (int i = 0; i < m; i++) {
    int x = R * cos(rr + tau / m * i);
    int y = R * sin(rr + tau / m * i);
    cout << x << " " << y << endl;
  }
  int r = rand();
  for (int i = 0; i < n - m; i++) {
    int x = 100.0 * i * i * sin(r + tau / (n - m) * i);
    int y = 100.0 * i * i * cos(r + tau / (n - m) * i);
    cout << x + 50 << " " << y + 150 << endl;
  }
  return 0;
}