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 = 1000000007;
const double INFD = 10e50;
const double EPS = 10e-9;
complex<double> comp_from_ang(double _ang) {
  complex<double> ret(1.0 / tan(_ang), 1);
  return ret / abs(ret);
}
vector<complex<double> > V;
int n, m;
double sgn(double x) {
  if (x > 0)
    return 1;
  else
    return -1;
}
void prog() {
  complex<double> A(10000000, 0), pObr = comp_from_ang(2.0 * M_PI / double(n));
  for (int i = 0; i < (n); ++i) {
    A *= pObr;
    V.push_back(A);
  }
  srand(time(NULL));
  static const complex<double> DWA(2, 0);
  for (int i = 0; i < (m - n); ++i) {
    complex<double> J(100000 + rand() % 1000, 10 + rand() % 4);
    A = V[i];
    A = A * DWA + J * sgn(A.real()) * sgn(A.imag());
    V.push_back((A));
  }
  for (int i = 0; i < (V.size()); ++i) {
    cout << int(V[i].real()) << " " << int(V[i].imag());
    if (i < V.size() - 1) cout << endl;
  }
}
void gencztery() {
  V.push_back(complex<double>(2, 0));
  V.push_back(complex<double>(0, 2));
  V.push_back(complex<double>(-2, 0));
  V.push_back(complex<double>(0, -2));
  V.push_back(complex<double>(4, 1));
  V.push_back(complex<double>(-1, 4));
  V.push_back(complex<double>(-4, -1));
  V.push_back(complex<double>(1, -4));
}
int main() {
  ios_base::sync_with_stdio(0);
  cin >> m >> n;
  if (n == 3) {
    if (m > 4)
      cout << "-1";
    else
      prog();
  }
  if (n == 4) {
    gencztery();
    for (int i = 0; i < (m); ++i)
      cout << V[i].real() << " " << V[i].imag() << endl;
  }
  if (n > 4) prog();
}