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 kMaxN = 200, kMaxM = 100;
int n, m;
const int kInf = 10000000, Inf = 1000000;
struct Point {
  int x, y;
  Point() {}
  Point(int x_, int y_) : x(x_), y(y_) {}
};
vector<Point> a, b;
int main() {
  scanf("%d%d", &n, &m);
  if (n >= 5 && m == 3) {
    puts("-1");
    return 0;
  }
  a.push_back(Point(-kInf, kInf)), a.push_back(Point(kInf, kInf));
  int k = 0, s = 0;
  for (int i = 1; i <= k; ++i) {
    a.push_back(Point(-kInf + k * i, kInf + s + (k - i + 1)));
    s += (k - i + 1);
  }
  k = m - 2 - k, s = 0;
  for (int i = 1; i <= k; ++i) {
    a.push_back(Point(-kInf + k * i, kInf - s - (k - i + 1)));
    s += (k - i + 1);
  }
  b.push_back(Point(-Inf, -kInf)), b.push_back(Point(Inf, -kInf));
  k = 0, s = 0;
  for (int i = 1; i <= k; ++i) {
    b.push_back(Point(-Inf + k * i, -kInf - s - (k - i + 1)));
    s += (k - i + 1);
  }
  k = m - 2 - k, s = 0;
  for (int i = 1; i <= k; ++i) {
    b.push_back(Point(-Inf + k * i, -kInf + s + (k - i + 1)));
    s += (k - i + 1);
  }
  for (int i = 0; i < m; ++i) printf("%d %d\n", a[i].x, a[i].y);
  for (int i = 0; i < n - m; ++i) printf("%d %d\n", b[i].x, b[i].y);
  return 0;
}