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: Time Limit Exceeded)

use proconio::input;
use std::cmp::max;

fn main() {
    input! {
        a: i64,
        b: i64,
        n: i64,
    }

    let f = F { a, b };

    let ans = if n >= b - 1 {
        f.f(b - 1)
    } else {
        let mut m = 0;
        for i in 1..=n {
            m = max(m, f.f(i));
        }
        m
    };

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

struct F {
    a: i64,
    b: i64,
}

impl F {
    fn f(&self, x: i64) -> i64 {
        let a = self.a;
        let b = self.b;
        (a * x) / b - a * (x / b)
    }
}