Problem:
Score : 400 points

Problem Statement

Given are integers A, B, and N.

Find the maximum possible value of floor(Ax/B) - A × floor(x/B) for a non-negative integer x not greater than N.

Here floor(t) denotes the greatest integer not greater than the real number t.

Constraints

1 ≤ A ≤ 10^{6}

1 ≤ B ≤ 10^{12}

1 ≤ N ≤ 10^{12}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

A B N

Output

Print the maximum possible value of floor(Ax/B) - A × floor(x/B) for a non-negative integer x not greater than N, as an integer.

Sample Input 1

5 7 4

Sample Output 1

2

When x=3, floor(Ax/B)-A×floor(x/B) = floor(15/7) - 5×floor(3/7) = 2. This is the maximum value possible.

Sample Input 2

11 10 9

Sample Output 2

9

Solution in Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.io.IOException;
import java.io.InputStream;
import java.util.NoSuchElementException;

public class Main {

  public static void main(String[] args) {
    FastScanner sc = new FastScanner();
    int a = sc.nextInt();
    long b = sc.nextLong();
    long n = sc.nextLong();
    double maxNumber = 0;
    for (long x = (long) b / a; x <= n; x++) {
      if ((long) x / b >= 1) {
        break;
      }
      double fx = Math.floor(a * x / b) - a * Math.floor(x / b);
      if (fx > maxNumber) {
        maxNumber = fx;
      }
    }
    System.out.println((long) maxNumber);
  }

}

class FastScanner {
  private final InputStream in = System.in;
  private final byte[] buffer = new byte[1024];
  private int ptr = 0;
  private int buflen = 0;

  private boolean hasNextByte() {
    if (ptr < buflen) {
      return true;
    } else {
      ptr = 0;
      try {
        buflen = in.read(buffer);
      } catch (IOException e) {
        e.printStackTrace();
      }
      if (buflen <= 0) {
        return false;
      }
    }
    return true;
  }

  private int readByte() {
    if (hasNextByte())
      return buffer[ptr++];
    else
      return -1;
  }

  private static boolean isPrintableChar(int c) {
    return 33 <= c && c <= 126;
  }

  public boolean hasNext() {
    while (hasNextByte() && !isPrintableChar(buffer[ptr]))
      ptr++;
    return hasNextByte();
  }

  public String next() {
    if (!hasNext())
      throw new NoSuchElementException();
    StringBuilder sb = new StringBuilder();
    int b = readByte();
    while (isPrintableChar(b)) {
      sb.appendCodePoint(b);
      b = readByte();
    }
    return sb.toString();
  }

  public long nextLong() {
    if (!hasNext())
      throw new NoSuchElementException();
    long n = 0;
    boolean minus = false;
    int b = readByte();
    if (b == '-') {
      minus = true;
      b = readByte();
    }
    if (b < '0' || '9' < b) {
      throw new NumberFormatException();
    }
    while (true) {
      if ('0' <= b && b <= '9') {
        n *= 10;
        n += b - '0';
      } else if (b == -1 || !isPrintableChar(b)) {
        return minus ? -n : n;
      } else {
        throw new NumberFormatException();
      }
      b = readByte();
    }
  }

  public int nextInt() {
    long nl = nextLong();
    if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
      throw new NumberFormatException();
    return (int) nl;
  }

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