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: Time Limit Exceeded)

<?php

list($a, $b, $n) = explode(' ', trim(fgets(STDIN)));

$limit = $b < $n ? $b - 1 : $n;
$max = 0;
for ($i = 1; $i <= $limit; ++$i) {
    $temp = (int)floor($i * $a / $b) - $a * (int)floor($i / $b);
    if ($temp > $max) {
        $max = $temp;
    }
}

echo $max;