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)

#![allow(unused_imports)]
use std::cmp::*;
use std::collections::*;
use itertools::Itertools;
use proconio::{input, marker::*};
use superslice::*;
fn main() {
    input! {
        a: u128, b: u128, n: u128,
    }
    let mut ans = 0;
    let mut al = b-1;
    while al <= n{
        let qq = a / b;
        let rr = a % b;
        let qql = al / b;
        let rrl = al % b;
        let left = rr * rrl / b + rr * qql + qq * al;
        let right = (al / b) * a;
        if left > right {
            ans = max(ans, left - right);
        }
        al += b;
    }
    let al = n;
    let qq = a / b;
    let rr = a % b;
    let qql = al / b;
    let rrl = al % b;
    let left = rr * rrl / b + rr * qql + qq * al;
    let right = (al / b) * a;
    if left > right {
        ans = max(ans, left - right);
    }


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