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", $number); // STDIN から数値を読み込む
//fscanf(STDIN, "%d %d", $number2,$number3); // STDIN から数値を読み込む

$arr = explode(' ', trim(fgets(STDIN)));
$A = $arr[0];
$B = $arr[1];
$N = $arr[2];

//$A = 11;
//$B = 6;
//$N = 9;
$old_data = 0;

for($x=1;$x<$N;$x++){

$data = floor($A*$x/$B) -$A*floor($x/$B);
if($data > $old_data){
$old_data = $data;
}
//echo "x = {$x}のとき {$data} old_data:{$old_data}<br>";

}


echo $old_data;



?>