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(dead_code, unused_imports, deprecated)]
use std::cmp::{max, min, Reverse};

use itertools::Itertools;

use maplit::*;

use proconio::{input, fastout};
use proconio::marker::*;

const INF: usize = 1_000_000_007;

#[fastout]
fn solve() {
  input! {
    a: usize, b: usize, n: usize,
  };

  let x = min(b - 1, n);
  println!("{}", (a * x) / b - a * (x / b));
}

fn main() {
  std::thread::Builder::new()
    .name("big stack size".into())
    .stack_size(32 * 1024 * 1024)
    .spawn(|| {
      solve();
    })
    .unwrap()
    .join()
    .unwrap();
}