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>
#define int long long int
#define ld long double
#define getFaster ios_base::sync_with_stdio(false),cin.tie(NULL),cout.tie(NULL)
#define rep(i,init,n) for(int i=init;i<n;i++)
#define rev(i,n,init) for(int i=n;i>=init;i--)
#define MAXN 200005
#define MOD2 998244353
#define MOD1 1e9+7
#define f first
#define s second
#define endl '\n'
#define pii pair<int,int>
#define piii pair<pii,int>
#define precise(i) cout<<fixed<<setprecision(i)
#define codejam cout<<"Case #"<<ii+1<<": ";
#define impossible cout<<"IMPOSSIBLE"<<endl;
#define error(s) throw runtime_error(s)
using namespace std;
const long double PI = atan(1.0)*4;
const int64_t INF=8e18;
const int32_t LOG=21;
const int MOD=MOD2;


int32_t main()
{ 
      getFaster;
      int tests=1;
      //cin>>tests;
      rep(ii,0,tests)
      {
          int a,b,n;
          cin>>a>>b>>n;
          int x=min(n,b-1);
          ld frac=(x*1.000*a)/b;
          int val=floor(frac);
          cout<<val<<endl;
      }

      return 0;                         
}

/*
 TIPS:
 1.) Check for corner cases (like 0 is exception case)
 2.) Check for global memory sizes,memory refreshments and its complexity 
 3.) Check for sorting criteria (if used 1-based indexing)
 4.) Check for numbers overflow (while multiplying and doing MOD)
 5.) Check for typecasting issues like int to float( while dividing numbers)
*/