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;
struct node {
  int x, y;
} q[210];
int main() {
  int n, m, i, x, y, temp, flag, xx, j, k = 0;
  scanf("%d%d", &n, &m);
  if (m == 3) {
    if (n == 5 || n == 6)
      printf("-1\n");
    else if (n == 4) {
      printf("0 0\n");
      printf("3 0\n");
      printf("0 3\n");
      printf("1 1\n");
    } else {
      printf("0 0\n");
      printf("3 0\n");
      printf("0 3\n");
    }
  } else {
    temp = m;
    q[++k].x = 0;
    q[k].y = 521;
    temp--;
    x = 0;
    while (1) {
      x += 17;
      q[++k].x = x;
      q[k].y = x * x + 521;
      temp--;
      if (temp == 0) break;
      q[++k].x = -x;
      q[k].y = x * x + 521;
      temp--;
      if (temp == 0) break;
    }
    temp = n - m;
    if (temp) {
      x = 0;
      y = -521;
      flag = 0;
      for (i = 1; i <= k; i++) {
        for (j = i + 1; j <= k; j++) {
          if ((q[i].x - x) * (q[j].y - y) == (q[j].x - x) * (q[i].y - y)) {
            flag = 1;
            break;
          }
        }
        if (flag == 1) break;
      }
      if (flag == 0) {
        temp--;
        q[++k].x = x;
        q[k].y = y;
      }
    }
    xx = 0;
    while (1) {
      if (temp == 0) break;
      xx += 17;
      x = -xx;
      y = (-1) * x * x - 521;
      flag = 0;
      for (i = 1; i <= k; i++) {
        for (j = i + 1; j <= k; j++) {
          if ((q[i].x - x) * (q[j].y - y) == (q[j].x - x) * (q[i].y - y)) {
            flag = 1;
            break;
          }
        }
        if (flag == 1) break;
      }
      if (flag == 0) {
        temp--;
        q[++k].x = x;
        q[k].y = y;
      }
      if (temp == 0) break;
      x = xx;
      y = (-1) * x * x - 521;
      flag = 0;
      for (i = 1; i <= k; i++) {
        for (j = i + 1; j <= k; j++) {
          if ((q[i].x - x) * (q[j].y - y) == (q[j].x - x) * (q[i].y - y)) {
            flag = 1;
            break;
          }
        }
        if (flag == 1) break;
      }
      if (flag == 0) {
        temp--;
        q[++k].x = x;
        q[k].y = y;
      }
    }
  }
  for (i = 1; i <= k; i++) printf("%d %d\n", q[i].x, q[i].y);
  return 0;
}