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: i64,
        b: i64,
        n: i64,
    }

    let (af, bf) = (a as f64, b as f64);

    let f = |x: f64| f64::floor(af / bf * x) - af * f64::floor(x / bf);

    let period = b as f64 / a as f64;

    let mut ans = -1e12;
    for i in 0..a {
        let x = f64::floor(period * (i as f64));

        if x as i64 > n {
            break;
        }

        ans = if ans >= f(x) { ans } else { f(x) };
    }
    println!("{}", ans);
}