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 Python (3.8.2) (judge verdict: Accepted)

###
# main
if(__name__ == '__main__'):
    # input
    a, b, n = map(int, input().split(" "))

    mod = n % b
    div = n // b

    x = n
    if div == 0:
        if mod == 0:
            x = n-1
    else:
        if mod == 0:
            x = n-1
        else:
            x = n-mod-1
    
    floor_ax_b = (a * x) // b
    floor_x_b = x // b

    ans = floor_ax_b - a * floor_x_b

    # output
    print(ans)
# else:
    # do nothing