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++ (Clang 10.0.0) (judge verdict: Time Limit Exceeded)

#include <iostream>
int main(){
    long long int a,b,n,c,d,e,f;
    c=d=e=0;
    f=1;
    std::cin>>a>>b>>n;
    if(b>=a)e=b;
    if(a>b)e=a;
    for(long long int i=e;i>1;i--){
        if(a%i==0&& b%i==0){
            f=i;
            break;
        }
    }
    for(long long int i=n;n>0;i--){
        c=a*i/b-a*(i/b);
        if(d<c)
            d=c;
        if(n-i>a*b/f)break;
    }
    std::cout<<d<<std::endl;
    return 0;
}