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: Accepted)

<?php
fscanf(STDIN, "%d %d %d", $a, $b, $n);
$t = [$n];
$x = $n - ($n % $b + 1);
//echo $x . PHP_EOL;
$cnt = 0;
for ($i = $x; $i > 0; $i -= $b, $cnt++) {
    if ($cnt > 10000) break;
    $t[] = $i;
    //echo $i . PHP_EOL;    
}
$ans = [];
foreach ($t as $v) {
    $ans[] = calc($a, $b, $v);
}
//var_dump($ans);
printf("%d", max($ans));
exit;

for ($i = 1; $i <= $n; $i++) {
    echo calc($a, $b, $i) . PHP_EOL;
}


function calc($a, $b, $n) {
    $c = intdiv($a * $n, $b);
    $d = $a * intdiv($n, $b);
    $e = $c - $d;
    //printf("n = %d , [ %d * %d ] / %d - %d * [ %d / %d ] , %d - %d\n", $n, $a, $n, $b, $a, $n, $b, $c, $d);
    return $e;
}