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 Haskell (GHC 8.8.3) (judge verdict: Accepted)

solve :: Int -> Int -> Int -> Int
solve a b n = floor $ point * fromIntegral a
  where x | n < b-1 = n
          | otherwise = b - 1
        y = (fromIntegral x) / (fromIntegral b)
        point = y - (fromIntegral . floor $ y)

main :: IO ()
main = do
  [a, b, n] <- map (read :: String -> Int) .words <$> getLine
  print $ solve a b n