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 C (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <stdio.h>

int f(int A, int B, int x)
{
    return (A * x) / B - A * (x / B);
}

int max(int a, int b) {
    if (a > b)
        return a;
    else
        return b;
}

int main(void)
{
    int A, B, N;
    scanf("%d%d%d", &A, &B, &N);

    int x, res;
    res = 0;
    for (x = 1; x <= N; ++x)
    {
        res = max(res, f(A, B, x));
    }

    printf("%d", res);

    return 0;
}