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 JAVA):

Solution:
import java.io.*;
import java.util.*;

public class cf227b {
  public static void main(String[] args) {
    FastIO in = new FastIO(), out = in;
    int n = in.nextInt();
    int m = in.nextInt();
    if(m == 3 && n >= 5) {
      out.println("-1");
      out.close();
      return;
    }

    int rad = (int)1e7;
    for(int i=0; i<m; i++) {
      double ang = (2*i*Math.PI)/m;
      int x = (int)(Math.cos(ang)*rad);
      int y = (int)(Math.sin(ang)*rad);
      out.println(x+" "+y);
    }
    rad /= 100;
    for(int i=0; i<n-m; i++) {
      double ang = (2*i*Math.PI + 1)/(n-m);
      int x = (int)(Math.cos(ang)*rad);
      int y = (int)(Math.sin(ang)*rad);
      out.println(x+" "+y);
    }
    out.close();
  }

  static class FastIO extends PrintWriter {
    BufferedReader br;
    StringTokenizer st;

    public FastIO() {
      this(System.in, System.out);
    }

    public FastIO(InputStream in, OutputStream out) {
      super(new BufferedWriter(new OutputStreamWriter(out)));
      br = new BufferedReader(new InputStreamReader(in));
      scanLine();
    }

    public void scanLine() {
      try {
        st = new StringTokenizer(br.readLine().trim());
      } catch (Exception e) {
        throw new RuntimeException(e.getMessage());
      }
    }

    public int numTokens() {
      if (!st.hasMoreTokens()) {
        scanLine();
        return numTokens();
      }
      return st.countTokens();
    }

    public String next() {
      if (!st.hasMoreTokens()) {
        scanLine();
        return next();
      }
      return st.nextToken();
    }

    public double nextDouble() {
      return Double.parseDouble(next());
    }

    public long nextLong() {
      return Long.parseLong(next());
    }

    public int nextInt() {
      return Integer.parseInt(next());
    }
  }
}