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 f(long long x) {
    return (a * x) / b - a * (x / b);
}

int main() {
    cin >> a >> b >> n;
    long long lo = 0, hi = n, mid;

    long long ans = 0;

    while (lo <= hi) {
        mid = (lo + hi) / 2;
        if (f(mid) >= ans) {
            lo = mid + 1;
            ans = f(mid);
        } else {
            hi = mid - 1;
        }
    }
    cout << ans << endl;
}