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 cond = 1;
int points[500][2];
int main() {
  int n, m;
  scanf("%d %d", &n, &m);
  if (m == 3) {
    if (n >= 5) {
      printf("-1\n");
      return 0;
    }
    if (n == 4) {
      printf("0 0\n10 0\n0 10\n1 1\n");
      return 0;
    }
    if (n == 3) {
      printf("0 0\n10 0\n0 10\n");
      return 0;
    }
  } else {
    points[0][0] = 0;
    points[0][1] = 0;
    for (int i = 1; i < (m + 2) / 2; ++i) {
      points[2 * i - 1][0] = points[2 * i - 2][0] + i;
      points[2 * i - 1][1] = i;
      points[2 * i][0] = points[2 * i - 1][0];
      points[2 * i][1] = -points[2 * i - 1][1];
    }
    int maxx = points[m - 1][0];
    for (int i = 0; i < m; ++i) {
      printf("%d %d\n", points[i][0] - maxx + 100000000, points[i][1]);
    };
    for (int i = 0; i < n - m; ++i) {
      printf("%d %d\n", maxx - points[i][0] + -100000000, points[i][1]);
    }
  }
}