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: Accepted)

use num::integer::gcd;
use proconio::{fastout, input};

#[fastout]
fn main() {
    input! {
        a: i128,
        b: i128,
        n: i128,
    }

    //    for x in 0..(n + 1) as usize {
    //        let x = x as i128;
    //        let l = (a * x) / b;
    //        let r = a * (x / b);
    //        let d = l - r;
    //        eprintln!("{} : {} - {} = {}", x, l, r, d);
    //
    //        let h = (a * x) % b;
    //        let k = (x) % b;
    //        dbg!(a * k - h);
    //        dbg!((a * k - h) / b);
    //    }

    // let g = gcd(a % b, b);
    // let aa = (a % b) / g;

    let y = (b - 1).min(n);
    println!("{}", (a * y) / b - a * (y / b));
}