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::{
    fastout, input,
    marker::{Bytes, Chars, Isize1, Usize1},
};

use num::integer::*;

fn f(a: isize, b: isize, i: isize) -> isize {
    return ((a * i) as f64 / b as f64) as isize - a * (i as f64 / b as f64) as isize;
}

fn main() {
    input! {
       a:isize,b:isize,n:isize
    }
    let mut ans = 0_isize;
    ans = std::cmp::max(ans, f(a, b, n));
    if n < 10000 {
        for i in 0..=n {
            ans = std::cmp::max(ans, f(a, b, i));
        }
    } else {
        let mut q = b - 1;
        let mut w = (n / b) * b - 1;
        let e = lcm(a, b) / a;
        let mut v = e;
        let mut o = (n / e) * e;
        let mut c = 0;
        while true {
            if q <= n {
                ans = std::cmp::max(ans, f(a, b, q));
            }
            if w > 0 {
                ans = std::cmp::max(ans, f(a, b, w));
            }
            if v - 1 <= n {
                ans = std::cmp::max(ans, f(a, b, v - 1));
            }
            if o - 1 > 0 {
                ans = std::cmp::max(ans, f(a, b, o - 1));
            }
            q += b;
            w -= b;
            c += 1;
            v += e;
            o -= e;
            if c > 10000000 {
                break;
            }
        }
    }
    println!("{}", ans);
}