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: Wrong Answer)

if __name__ == '__main__':
    from sys import stdin
    # from collections import defaultdict
    import math
    input = stdin.readline

    a, b, n = map(int, input().split())
    if b > n:
        print(int(math.floor(a*n/b)-a*math.floor(n/b)))
        exit()

    if b >= 10**6:
        ans = 0
        for i in (b-1, n+1, b):
            temp =  math.floor(a*i/b)-a*math.floor(i/b)
            if ans < temp:
                ans = temp
        print(int(ans))
        exit()

    ans = int(math.floor(a*n/b)-a*math.floor(n/b))
    i = math.floor(n/b)*b-1
    for _ in range(10**6):
        temp =  math.floor(a*i/b)-a*math.floor(i/b)
        if ans < temp:
            ans = temp
        i -= b
    print(int(ans))