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: Accepted)

import scala.io.StdIn

object Main extends App {

  val Array(a, b, n) = StdIn.readLine().split(" ").map(_.toLong)
  val x = if (b > 1) n / (b - 1) * (b - 1) else 0
  println(if (x > 0) f(x) else f(n))

  def f(x: Long) = (a * x) / b - a * (x / b)

  def readIntPair: (Int, Int) = {
    val Array(x, y) = StdIn.readLine().split(" ").map(_.toInt)
    (x, y)
  }

  def readIntArr = StdIn.readLine().split(" ").map(_.toInt)
}