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 proconio::{fastout, input};
use std::cmp;

#[fastout]
fn main() {
    input! {
        a: i64,
        b: i64,
        n: i64,
    }
    let mut ans = 0;
    let mut l = 0;
    let mut r = cmp::min(n, b - 1);

    // // fail
    // for i in 1..(n + 1) {
    //     let x = a * i / b - a * (i / b);
    //     if x > ans {
    //         ans = x;
    //     }
    //     println!("{}", x);
    // }

    // bin search
    // while (r - l).abs() > 1 {
    //     // println!("test");
    //     let m = (r - l) / 2;
    //     let x = a * (m % b) - (a * m % b);
    //     println!("{} {}", m, x);
    //     if x > ans {
    //         l = m;
    //         ans = x;
    //     } else if x < ans {
    //         r = m;
    //     }
    // }
    let x = cmp::min(n, b - 1);
    let ans = a * x / b - a * (x / b);
    println!("{}", ans);
}