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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
#[allow(unused_imports)]
use std::cmp;

fn run() {
    let (r, w) = (std::io::stdin(), std::io::stdout());
    let mut sc = IO::new(r.lock(), w.lock());

    let a: usize = sc.read();
    let b: usize = sc.read();
    let n: usize = sc.read();

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

fn main() {
    std::thread::Builder::new()
        .name("run".into())
        .stack_size(256 * 1024 * 1024)
        .spawn(run)
        .unwrap()
        .join()
        .unwrap();
}

pub struct IO<R, W: std::io::Write>(R, std::io::BufWriter<W>);

impl<R: std::io::Read, W: std::io::Write> IO<R, W> {
    pub fn new(r: R, w: W) -> IO<R, W> {
        IO(r, std::io::BufWriter::new(w))
    }
    pub fn write<S: std::ops::Deref<Target = str>>(&mut self, s: S) {
        use std::io::Write;
        self.1.write(s.as_bytes()).unwrap();
    }
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .0
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r' || b == b'\t')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r' && b != b'\t')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn read_vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn read_pairs<T: std::str::FromStr>(&mut self, n: usize) -> Vec<(T, T)> {
        (0..n).map(|_| (self.read(), self.read())).collect()
    }
    pub fn read_chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
    pub fn read_char_grid(&mut self, n: usize) -> Vec<Vec<char>> {
        (0..n).map(|_| self.read_chars()).collect()
    }
    pub fn read_matrix<T: std::str::FromStr>(&mut self, n: usize, m: usize) -> Vec<Vec<T>> {
        (0..n)
            .map(|_| (0..m).map(|_| self.read()).collect())
            .collect()
    }
}

#[allow(dead_code)]
fn yn(flag: bool) {
    if flag {
        println!("Yes");
    } else {
        println!("No");
    }
}

use std::ops::{Add, Div};

/// Generic binary search
///
/// # Arguments
///
/// * `l` - the value assumes to `pred(l) = true`
/// * `r` - the value assumes to `pred(r) = false`
/// * `pred` - predicate for binary search
///
/// # Returns
///
/// * `ret` where `pred(ret) = true` && `pred(ret + delta) = false`
///
/// # Note
///
/// `pred(l)` and `pred(r)` are not called. `pred` is called only values in the range `(l, r)`.
///
pub fn binary_search<T: Add<Output = T> + Div<Output = T> + PartialEq + From<u8> + Copy>(
    l: T,
    r: T,
    pred: impl Fn(T) -> bool,
) -> T {
    let mut l = l;
    let mut r = r;
    let two = T::from(2_u8);
    loop {
        let m = (l + r) / two;
        if l == m || r == m {
            break l;
        }
        if pred(m) {
            l = m;
        } else {
            r = m;
        }
    }
}

#[test]
fn binary_search_test() {
    let v = [1, 2, 3, 4, 5];
    assert_eq!(3, binary_search(v.len() as _, -1, |i| v[i as usize] > 3));
    assert_eq!(5, binary_search(v.len() as _, -1, |i| v[i as usize] > 100));
    assert_eq!(0, binary_search(v.len() as _, -1, |i| v[i as usize] > 0));
}

/// Returns index to the first element in `v` which does not compare less than `val`.
pub fn lower_bound<T: PartialOrd>(v: &[T], val: &T) -> usize {
    (binary_search(-1, v.len() as i64, |i: i64| v[i as usize] < *val) + 1) as usize
}

#[test]
fn lower_bound_test() {
    let v = vec![1, 3, 3, 4, 5];
    assert_eq!(lower_bound(&v, &0), 0);
    assert_eq!(lower_bound(&v, &1), 0);
    assert_eq!(lower_bound(&v, &2), 1);
    assert_eq!(lower_bound(&v, &3), 1);
    assert_eq!(lower_bound(&v, &4), 3);
    assert_eq!(lower_bound(&v, &5), 4);
    assert_eq!(lower_bound(&v, &999), 5);
}

/// Returns index to the first element in `v` which compares greater than `val`.
pub fn upper_bound<T: PartialOrd>(v: &[T], val: &T) -> usize {
    (binary_search(-1, v.len() as i64, |i: i64| v[i as usize] <= *val) + 1) as usize
}

#[test]
fn upper_bound_test() {
    let v: &[i32] = &[1, 3, 3, 4, 5];
    assert_eq!(upper_bound(v, &0), 0);
    assert_eq!(upper_bound(v, &1), 1);
    assert_eq!(upper_bound(v, &2), 1);
    assert_eq!(upper_bound(v, &3), 3);
    assert_eq!(upper_bound(v, &4), 4);
    assert_eq!(upper_bound(v, &5), 5);
    assert_eq!(upper_bound(v, &999), 5);
}

/// Returns `(lower_bound(v, val), upper_bound(v, val))`
pub fn equal_range<T: PartialOrd>(v: &[T], val: &T) -> (usize, usize) {
    (lower_bound(v, val), upper_bound(v, val))
}

pub fn gcd(a: usize, b: usize) -> usize {
    if b == 0 {
        a
    } else {
        gcd(b, a % b)
    }
}
*/

fn main() {
    let exe = "/tmp/bin3707B78A";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";