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;
    cin >> a >> b >> n;

    long long ans = 0;

    if (n<b){
        ans = (long long)(a*n/b) - a*(long long)(n/b);
    }else{
        if (n%b==0){
            ans = (long long)(a*(n-1)/b) - a*(long long)((n-1)/b);
        }else{
            ans = (long long)(a*(n-n%b-1)/b) - a*(long long)((n-n%b-1)/b);
        }
    }
    cout << ans << endl;
}