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)

a, b, n = map(int, input().split())

cnt = 1
buf = []
buf.append(int(a * n / b) - a * (int(n / b)))

while True:
    if n / b > 10 ** 6:
        break
    x = cnt * b - 1
    if n < x :
        break
    calc = int(a * x / b) - a * (int(x / b))
    if calc > max(buf):
        buf.append(calc)
    cnt += 1
    
if n / b > 10 ** 6:
    ans = b -1

ans = max(buf)
print(ans)