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 = 3.1415926535897932384626;
const double R = 9e7;
const double r = 8e7;
int m, n;
int main() {
  cin >> n >> m;
  if (m == 3) {
    if (n <= 4) {
      cout << "0 0\n";
      cout << "3 0\n";
      cout << "0 3\n";
      if (n == 4) cout << "1 1\n";
    } else {
      cout << "-1\n";
    }
  } else if (m == 4) {
    cout << "0 0\n";
    cout << "9 0\n";
    cout << "0 3\n";
    cout << "9 3\n";
    if (n >= 5) cout << "1 1\n";
    if (n >= 6) cout << "1 2\n";
    if (n >= 7) cout << "8 1\n";
    if (n == 8) cout << "8 2\n";
  } else {
    int nextodd = (m % 2 == 0) ? m + 1 : m;
    for (int i = 0; i < m; i++) {
      double angle = (2 * PI / nextodd) * i;
      cout << (int)(R * cos(angle)) << " " << (int)(R * sin(angle)) << endl;
    }
    for (int i = m + 1; i <= n; i++) {
      double angle = (2 * PI / nextodd) * i;
      cout << (int)(r * cos(angle)) << " " << (int)(r * sin(angle)) << endl;
    }
  }
  return 0;
}