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 <iostream>
#include <string>
#include <map>
#include <algorithm>
#include <vector>

#define ll long long

int main()
{
    ll A, B, N;
    std::cin >> A >> B >> N;

    // xはB以下になると思われる(0になるから)
    ll max = 0;
    ll x = N-4;

    if(N >= B) {
        max = (A * (B-1)) / B;
        //std::cout << max << std::endl;
    }
    else {
        max = A * N / B - A * (N / B);
    }
    std::cout << max << std::endl;
}