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 Rust (1.42.0) (judge verdict: Wrong Answer)

use proconio::input;

fn main() {
    input! {
        a: usize,
        b: usize,
        n: usize,
    }

    if n < 10e9 as usize {
        println!("{}", (0..=b.min(n)).map(|x| f(a, b, x)).max().unwrap());
    } else {
        let (mut left, mut right) = (0, b.min(n));
        while right > left {
            let mid = (left + right) / 2;
            let (left_value, mid_value) = (f(a, b, left), f(a, b, mid));
            if left_value < mid_value {
                left = mid;
            } else {
                right = mid;
            }
        }

        println!("{}", f(a, b, right).max(f(a, b, right + 1)));
    }
}

fn f(a: usize, b: usize, x: usize) -> usize {
    a * x / b - a * (x / b)
}