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>
#pragma comment(linker, "/STACK:256000000")
using namespace std;
int n, m;
const double pi = 2 * acos(0.);
int main() {
  cin >> n >> m;
  if (m == 3 && n >= 5) {
    cout << -1 << endl;
    return 0;
  }
  if (m == 4 && n == 7) {
    cout << "176166 6377\n709276 539564\n654734 174109\n910147 434207\n790497 "
            "366519\n606663 21061\n859328 886001"
         << endl;
    return 0;
  }
  if (m == 4 && n == 8) {
    cout << "0 0\n8 0\n8 3\n0 3\n2 1\n2 2\n6 1\n6 2" << endl;
    return 0;
  }
  double diam = 1e7;
  vector<pair<int, int> > v;
  for (int i = 0; i < m; ++i) {
    double cx = diam * cos(2. * i * pi / m);
    double cy = diam * sin(2. * i * pi / m);
    printf("%d %d\n", (int)(cx), (int)(cy));
    v.push_back(make_pair(cx, cy));
  }
  diam /= 100;
  int dx = (rand() % 100 + 37) + 2 * diam;
  int dy = rand() % 100 + 24 + 2 * diam;
  for (int i = 0; i < n - m; ++i) {
    double cx = diam * cos(2. * i * pi / m) + dx;
    double cy = diam * sin(2. * i * pi / m) + dy;
    printf("%d %d\n", (int)(cx), (int)(cy));
    v.push_back(make_pair(cx, cy));
  }
  return 0;
}