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: Time Limit Exceeded)

use proconio::input;

fn main() {
        input! {
                a: i64,
                b: i64,
                n: i64,
        }
        let ans: i64 = (0..n + 1)
                .map(|x| {
                        (a as f64 * x as f64 / b as f64).floor() - a as f64 * (x as f64 / b as f64).floor()
                })
                .map(|x| x as i64)
                .max().unwrap();

        println!("{}", ans)
}