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_mut)]
#![allow(non_snake_case)]
#![allow(unused_variables)]
#![allow(unused_imports)]
#![allow(dead_code)]
macro_rules! input {
  (source = $s:expr, $($r:tt)*) => {
    let mut iter = $s.split_whitespace();
    let mut next = || { iter.next().unwrap() };
    input_inner!{next, $($r)*}
  };
  ($($r:tt)*) => {
    let stdin = std::io::stdin();
    let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
    let mut next = move || -> String{
      bytes
        .by_ref()
        .map(|r|r.unwrap() as char)
        .skip_while(|c|c.is_whitespace())
        .take_while(|c|!c.is_whitespace())
        .collect()
    };
    input_inner!{next, $($r)*}
  };
}
macro_rules! input_inner {
  ($next:expr) => {};
  ($next:expr, ) => {};

  ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
    let $var = read_value!($next, $t);
    input_inner!{$next $($r)*}
  };
}
macro_rules! read_value {
  ($next:expr, ( $($t:tt),* )) => {
    ( $(read_value!($next, $t)),* )
  };

  ($next:expr, [ $t:tt ; $len:expr ]) => {
    (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
  };

  ($next:expr, chars) => {
    read_value!($next, String).chars().collect::<Vec<char>>()
  };

  ($next:expr, usize1) => {
    read_value!($next, usize) - 1
  };

  ($next:expr, $t:ty) => {
    $next().parse::<$t>().expect("Parse error")
  };
}

fn main() {
  input!{
    A: u128,
    B: u128,
    N: u128,
  }
  let ans = if B > N {
    (A * N) / B - A * (N / B)
  } else if B == N {
    (A * (N-1)) / B - A * ((N-1) / B)
  } else {
    (A * (B-1)) / B - A * ((B-1) / B)
  };

  // for x in 0..N+1 {
  //   let i = (A * x) / B - A * (x / B);
  //   println!("{}: {}", x, i);
  // }

  println!("{}", ans);
}