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: Runtime Error)

#include<iostream>
//#include<cmath>
//#include<algorithm>
using namespace std;

int main(){
	long long int A, B, N, i, x;
	cin >> A >> B >> N;
	long long int end = N/(B-1)+1;
	
	int max = (A*N/B) - A*(N/B);
	
	for(i=1; i<=end; i++){
		x = (B-1)*i;
		if(x<=N){
			int floor = (A*x/B) - A*(x/B);
			if(floor > max)	max = floor;
		}
	}
	
	cout << max << endl;
	
	return 0;
}