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 PHP (7.4.4) (judge verdict: Wrong Answer)

<?php
  	fscanf(STDIN, "%d %d %d", $A, $B, $N);
	$max = 1;
	for ($x=1;$x<=$N;$x++) {
    	$value = floor($A*$x/$B) - $A*floor($x/$B);	
      	if ($value > $max) {
          	$max = $value;
        }
    }

	echo $max . "\n";