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;
long long a,b,n;
long long check(long long x)
{
	return a*x/b-a*(x/b);
}
int main()
{
	cin>>a>>b>>n;
	long long l=0,r=n,ans=0;
	while(r-l>=1000000)
	{
		long long lmid=l+(r-l)/3,rmid=r-(r-l)/3;
		if(check(lmid)<=check(rmid))
			l=lmid;
		else
			r=rmid;
	}
	while(l<=r&&l<=n)
	{
		ans=max(ans,check(l));
		l++;
	}
	cout<<ans<<endl;
	return 0;
}