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: Accepted)

#include <iostream>

using namespace::std;

int main()
{
    long long A, B, N, i;
    cin >> A >> B >> N;
    if(N < B){
        cout << A*N/B - A*(N/B);
    }else if(A >= B){
        if(N%B == 0)
            cout << A*(N-1)/B - A*((N-1)/B);
        else
            cout << A*N/B - A*(N/B);
    }else{
        i = N/B*B - 1;
        cout << A*i/B - A*(i/B);
    }
}