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
  $s = trim(fgets(STDIN));
  $s = str_replace(array("\r\n","\r","\n"), '', $s);
  $s = explode(" ", $s);
    // x = 3のとき、floor(Ax/B)−A × floor(x/B) = floor(15/7)−5 × floor(3/7)=2  となります
    
    //A B N
    // var_dump($s);
    $A = (int)$s[0]; 
    $B = (int)$s[1]; 
    $N = (int)$s[2];
    
    $maximum = 0;
    $calc = 0;
    $prev = -1;
    
    $is1 = true;
    $is2 = true;
    
    for ($i = $N; $i >= 1; --$i){
        if ($is1) {
            $calc = floor($A*$i/$B)-$A * floor($i/$B);
        }
        if ($is2) {
            $i2 = $N - $i;
            $calc2 = floor($A*$i2/$B)-$A * floor($i2/$B);
        }
        
        if ($is1 && $is2) {
            if ($i < $i2) {
                $ans = $i2;
                $is1 = false;
            } else {
                 $ans = $i;
                 $is2 = false;
            }
        }
        
        if ($prev == $ans) {
            break;
        }
        
        if ($maximum <= $ans) {
            $maximum = $ans;
        }
        $prev = $ans;
        
        
    }
    
    echo $maximum;


  ?>