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 int INF = int(1e9);
const double EPS = 1e-5;
const long long mod = ((long long)1e18) - 131;
int n, m, k, x = 0, y = 0, ans = 0, r = 1, e = 1, h = 0, plc;
vector<pair<int, int> > u;
vector<pair<int, int> > d;
int main() {
  srand(time(NULL));
  scanf("%d %d", &n, &m);
  if (m == 3 && n > 4) {
    cout << -1;
    return 0;
  }
  x = 0;
  y = 10000000;
  for (int i = 0; i <= 100; i++) {
    u.push_back(make_pair(x, y));
    d.push_back(make_pair(x, -y));
    if (x) {
      u.push_back(make_pair(-x, y));
      d.push_back(make_pair(-x, -y));
    }
    x++;
    y += e;
    e += rand() % 1000;
  }
  for (int i = 0; i < m; i++) {
    printf("%d %d\n", u[i].first, u[i].second);
  }
  for (int i = 0; i < n - m; i++) {
    printf("%d %d\n", d[i].first, d[i].second);
  }
  return 0;
}