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 = 1e9;
const int MOD = 1e9 + 7;
const int N = 0;
int n, m;
void solve() {
  if (m == 3 && n > 4) {
    printf("-1");
    return;
  };
  if (m == 4 && n == 8) {
    printf("0 0\n0 1\n1 1\n1 0\n-1 -2\n-1 3\n2 -2\n2 3\n");
    return;
  }
  printf("100000 1000\n");
  for (auto i = 1; i < m; i++)
    printf("%d %d\n", 100000 + i * (i + 1) / 2, 1000 - i);
  if (n - m) {
    int dec = (n == 2 * m) ? 1 : 0;
    if (dec) printf("100000 0\n");
    for (auto i = 1; i <= n - m - dec; i++)
      printf("%d %d\n", 10000 - i * (i + 1) / 2, 1000 - i);
  }
}
int main() {
  cin >> n >> m;
  solve();
}