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 Scala (2.13.1) (judge verdict: Time Limit Exceeded)

import java.io.{BufferedOutputStream, BufferedReader, InputStreamReader, PrintWriter}

object Main {
  def main(args: Array[String]): Unit = {
    val in = new BufferedReader(new InputStreamReader(System.in))
    val out = new PrintWriter(new BufferedOutputStream(System.out))
    val (a, b, n) = in.readLine().split("\\s+") match {
      case Array(a, b, n) => (a.toLong, b.toLong, n.toLong)
    }

    var max = Long.MinValue
    var x = if (b - 1 < n) {
      b - 1
    } else {
      n
    }

    while (x <= n) {
      max = Math.max(max, a * x / b - a * (x / b))
      x += b
    }

    out.println(max)
    out.flush()
  }
}