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;
vector<pair<int, int> > P, A;
int pos, x, y, delta, R, N, M, i;
int main() {
  cin >> N >> M;
  if (M == 3) {
    if (N == 6) {
      cout << -1 << endl;
      return 0;
    }
    if (N == 5) {
      cout << -1 << endl;
      return 0;
    }
    if (N == 3) {
      cout << "0 0" << endl;
      cout << "3 0" << endl;
      cout << "0 3" << endl;
      return 0;
    }
    if (N == 4) {
      cout << "0 0" << endl;
      cout << "3 0" << endl;
      cout << "0 3" << endl;
      cout << "1 1" << endl;
      return 0;
    }
    return 0;
  }
  if (M == 4) {
    cout << "0 0" << endl;
    cout << "10 0" << endl;
    cout << "0 10" << endl;
    cout << "10 10" << endl;
    P.push_back(make_pair(-1, -2));
    P.push_back(make_pair(-100, 102));
    P.push_back(make_pair(11, 27));
    P.push_back(make_pair(1323123, -423232));
    for (i = 0; i < N - M; i++)
      cout << P[i].first << " " << P[i].second << endl;
    return 0;
  }
  for (i = 0; i < M; i++) cout << -100000000 + i << " " << i * i << endl;
  for (i = 0; i < N - M; i++) cout << 100000000 - i << " " << -i * i << endl;
}