You are given two integers n and k.

You need to construct k regular polygons having same [circumcircle](https://en.wikipedia.org/wiki/Circumscribed_circle), with distinct number of sides l between 3 and n. 

<image> Illustration for the first example.

You can rotate them to minimize the total number of distinct points on the circle. Find the minimum number of such points.

Input

The only line of input contains two integers n and k (3 ≤ n ≤ 10^{6}, 1 ≤ k ≤ n-2), the maximum number of sides of a polygon and the number of polygons to construct, respectively.

Output

Print a single integer — the minimum number of points required for k polygons.

Examples

Input


6 2


Output


6


Input


200 50


Output


708

Note

In the first example, we have n = 6 and k = 2. So, we have 4 polygons with number of sides 3, 4, 5 and 6 to choose from and if we choose the triangle and the hexagon, then we can arrange them as shown in the picture in the statement.

Hence, the minimum number of points required on the circle is 6, which is also the minimum overall possible sets.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in Actual solution is at the top
 *
 * @author ilyakor
 */
public class Main {

  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    InputReader in = new InputReader(inputStream);
    OutputWriter out = new OutputWriter(outputStream);
    TaskG solver = new TaskG();
    solver.solve(1, in, out);
    out.close();
  }

  static class TaskG {

    public void solve(int testNumber, InputReader in, OutputWriter out) {
      int n = in.nextInt();
      int k = in.nextInt();
      int[] phi = new int[n + 1];
      for (int i = 2; i <= n; ++i) {
        if (phi[i] == 0) {
          phi[i] = i - 1;
          for (int j = i * 2; j <= n; j += i) {
            if (phi[j] == 0) {
              phi[j] = j;
            }
            phi[j] = phi[j] / i * (i - 1);
          }
        }
      }
      Arrays.sort(phi, 3, phi.length);
      long res = 2;
      for (int i = 0; i < k; ++i) {
        res += phi[3 + i];
      }
      if (k == 1) {
        --res;
      }
      // if (k == 2) {
      //     // We're taking
      // }
      out.printLine(res);
    }

  }

  static class OutputWriter {

    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
      writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
      this.writer = new PrintWriter(writer);
    }

    public void print(Object... objects) {
      for (int i = 0; i < objects.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(objects[i]);
      }
    }

    public void printLine(Object... objects) {
      print(objects);
      writer.println();
    }

    public void close() {
      writer.close();
    }

  }

  static class InputReader {

    private InputStream stream;
    private byte[] buffer = new byte[10000];
    private int cur;
    private int count;

    public InputReader(InputStream stream) {
      this.stream = stream;
    }

    public static boolean isSpace(int c) {
      return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public int read() {
      if (count == -1) {
        throw new InputMismatchException();
      }
      try {
        if (cur >= count) {
          cur = 0;
          count = stream.read(buffer);
          if (count <= 0) {
            return -1;
          }
        }
      } catch (IOException e) {
        throw new InputMismatchException();
      }
      return buffer[cur++];
    }

    public int readSkipSpace() {
      int c;
      do {
        c = read();
      } while (isSpace(c));
      return c;
    }

    public int nextInt() {
      int sgn = 1;
      int c = readSkipSpace();
      if (c == '-') {
        sgn = -1;
        c = read();
      }
      int res = 0;
      do {
        if (c < '0' || c > '9') {
          throw new InputMismatchException();
        }
        res = res * 10 + c - '0';
        c = read();
      } while (!isSpace(c));
      res *= sgn;
      return res;
    }

  }
}

