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 INP, AM, REACHEOF;
char BUF[(1 << 12) + 1], *inp = BUF;
const double PI = acos((double)-1.0);
int M;
void print(int n, double x0, double y0, int sz) {
  double alpha = PI * 2 / M, cur = 0.0;
  if (x0 > 1) cur = 0.01;
  for (int i = (1), _b = (n); i <= _b; i++) {
    cur += alpha;
    double x = cos(cur) * sz + x0;
    double y = sin(cur) * sz + y0;
    cout << (int)(round(x + 1e-6)) << ' ' << (int)(round(y + 1e-6)) << endl;
  }
}
int main() {
  int n, m;
  while (cin >> n >> m) {
    M = m;
    if (m == 3) {
      if (n == 3) {
        cout << "0 0\n0 1\n1 0\n";
      } else if (n == 4) {
        cout << "0 0\n3 0\n0 3\n1 1\n";
      } else
        puts("-1");
    } else {
      print(m, 0, 0, 10000000);
      if (n > m) print(n - m, 50, 50, 8000000);
    }
    break;
  }
  return 0;
}