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<bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0;i<(n);i++)
#define rrep(i,m,n) for(int i=(m);i<(n);i++)
#define fore(i,a) for(auto &i:a)
#define debug(a,b) cout << "debug : " << a << " , "<< b << endl
using ll=long long;
const ll INF=1LL<<60;
const ll mod=1E9+7;


int main(){
  ll a,b,n;
  cin >> a >> b >> n;
  ll M=0;
  for(int k=n;k>max(n-b,(ll)0);k--){
    int kb=k/b;
    if(a*k/b-a*kb>M)M=a*k/b-a*kb;
    debug(k,a*k/b-a*kb);
  }
  cout << M;
}