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 JavaScript (Node.js 12.16.1) (judge verdict: Time Limit Exceeded)

function main(input) {
    const parsedInput = parser(input);
    console.log(minX(parsedInput.a, parsedInput.b, parsedInput.n));
}

function parser(inputStr) {
    const splitInput = inputStr.split(' ');
    return {
        a: Number(splitInput[0]),
        b: Number(splitInput[1]),
        n: Number(splitInput[2]),
    };
}

function minX(a, b, n) {
    const results = [];
    for (var x = 1; x <= n; x++ ){
        results.push(Math.floor((a * x) / b) - a * Math.floor(x / b));
    }
    return Math.max(...results);
}
// test
// const Q1 = '5 7 4'
// const Q2 = '11 10 9';
// main(Q1);
// main(Q2);
// main(Q2);
// main(Q3);
main(require('fs').readFileSync('/dev/stdin', 'utf8'));