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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

def main():
  import math
  a, b, n = map(int, input().split())
  gcd = math.gcd(a, b)
  a = int(a / gcd)
  b = int(b / gcd)
  ans = 0
  for i in range(min(b+1, n+1)):
    tmp = math.floor(a*i/b) - a*math.floor(i/b)
    if tmp > ans:
      ans = int(tmp)
  print(ans)
  
if __name__ == '__main__':
  main()