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 <bits/stdc++.h>
using namespace std;
typedef long long int ll;
int main () 
{
    ll a,b,n,k,ans=0,ans1=0;cin>>a>>b>>n;
    if (b==1) {
     ans1=0;
    }
    else {
      for (ll i=1;i<=100000;i++) {
        k=b*i-1;
        if (k<n) {
           ans=(a*k)/b - a*(i-1);
           ans1=max(ans,ans1);
        }
        else {
           ans=(a*n)/b - a*(i-1);
           ans1=max(ans,ans1);
           break;
        }
      }

    }
    cout<<ans1<<endl;
}