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: Time Limit Exceeded)

import qualified Data.Vector.Unboxed as V
import qualified Data.List as L


toInt x = read x :: Int
toFloat x = read x :: Float

func :: Float -> Float -> Int -> Float
func a b x = a * (xb - fromIntegral (floor xb))
     where
          xb = (fromIntegral x) / b

main = do
     abn <- map toInt . words <$> getLine
     let a = fromIntegral $ head abn
         b = fromIntegral $ abn !! 1
         n = last abn
     print $ floor $ V.maximum $ V.map (func a b) $ V.fromList [1..n]