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: Wrong Answer)

#[allow(unused_imports)]
use std::io::{stdout, Write, BufWriter};
#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use proconio::marker::{Isize1, Usize1, Bytes, Chars};

#[proconio::fastout]
fn main() {
    proconio::input!{
        a: i64,
        b: i64,
        n: i64,
    }
    let mut ans = 0;
    let g = gcd(a,b);
    let (a, b) = (a / g, b/ g);
    for r in (b * (multiples(0..n, b) - 1))..(n + 1) {
        ans = max(ans, (a * r) / b);
    }
    println!("{}", ans);
}

type SomeInt = i64;
fn gcd(x: SomeInt, y: SomeInt) -> SomeInt {
    if y == 0 {
        x
    } else {
        gcd(y, x % y)
    }
}

use std::ops::Range;
fn multiples(r: Range<SomeInt>, n: SomeInt) -> SomeInt {
    r.end / n - ((((r.start + n - 1))/ n) - 1)
}