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)

#![allow(unused)]

fn solve<R: std::io::BufRead>(mut sc: Scanner<R>) {
    let a: i64 = sc.get();
    let b: i64 = sc.get();
    let n: i64 = sc.get();

    if n < b {
        println!("{}", a * n / b );
    } else {
        println!("{}", a * (b - 1) / b);
    }
}

macro_rules! debug {
    ($($a:expr),*) => {
        eprintln!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
    }
}

//
// Based on EbTech's Scanner https://stackoverflow.com/q/56449027
//
struct Scanner<'a, R: std::io::BufRead> {
    reader: R,
    buf: String,
    iter: std::str::SplitWhitespace<'a>,
}

impl<'a, R: std::io::BufRead> Scanner<'a, R> {
    fn new(reader: R) -> Self {
        Self { reader, buf: String::new(), iter: "".split_whitespace() }
    }

    fn get<T: std::str::FromStr>(&mut self) -> T {
        if let Some(t) = self.iter.next() {
            return t.parse().ok().expect("Parse error")
        }
        self.buf.clear();
        self.reader.read_line(&mut self.buf).expect("I/O error");
        self.iter = unsafe { std::mem::transmute(self.buf.split_whitespace()) };
        self.get()
    }

    fn gets<T: std::iter::FromIterator<char>>(&mut self) -> T {
        use std::io::Read;
        assert_eq!(self.iter.next(), None);
        self.reader
            .by_ref()
            .bytes()
            .map(|b| b.unwrap() as char)
            .skip_while(|&c| c.is_whitespace())
            .take_while(|&c| !c.is_whitespace())
            .collect()
    }
}

fn main() {
    let stdin = std::io::stdin();
    solve(Scanner::new(stdin.lock()));
}