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) {
    var input = _input.split(" ");
    var num_A = parseInt(input[0]);
    var num_B = parseInt(input[1]);
    var num_N = parseInt(input[2]);
    var num_MaxVal = num_A <= num_B? num_A - 1 : num_B - 1;
    var result = 0;
    for( var x = 0 ; x <= num_N; x++ ) {
        y = Math.floor(num_A * x / num_B) - num_A * Math.floor( x / num_B );
        result = result < y? y:result;
        if( result == num_MaxVal ) break;
    }
    console.log(result);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));