Problem:
Score : 300 points

Problem Statement

Find the price of a product before tax such that, when the consumption tax rate is 8 percent and 10 percent, the amount of consumption tax levied on it is A yen and B yen, respectively. (Yen is the currency of Japan.)

Here, the price before tax must be a positive integer, and the amount of consumption tax is rounded down to the nearest integer.

If multiple prices satisfy the condition, print the lowest such price; if no price satisfies the condition, print -1.

Constraints

1 \leq A \leq B \leq 100

A and B are integers.

Input

Input is given from Standard Input in the following format:

A B

Output

If there is a price that satisfies the condition, print an integer representing the lowest such price; otherwise, print -1.

Sample Input 1

2 2

Sample Output 1

25

If the price of a product before tax is 25 yen, the amount of consumption tax levied on it is:

When the consumption tax rate is 8 percent: \lfloor 25 \times 0.08 \rfloor = \lfloor 2 \rfloor = 2 yen.

When the consumption tax rate is 10 percent: \lfloor 25 \times 0.1 \rfloor = \lfloor 2.5 \rfloor = 2 yen.

Thus, the price of 25 yen satisfies the condition. There are other possible prices, such as 26 yen, but print the minimum such price, 25.

Sample Input 2

8 10

Sample Output 2

100

If the price of a product before tax is 100 yen, the amount of consumption tax levied on it is:

When the consumption tax rate is 8 percent: \lfloor 100 \times 0.08 \rfloor = 8 yen.

When the consumption tax rate is 10 percent: \lfloor 100 \times 0.1 \rfloor = 10 yen.

Sample Input 3

19 99

Sample Output 3

-1

There is no price before tax satisfying this condition, so print -1.

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

{-# LANGUAGE BangPatterns, OverloadedStrings #-}

import Control.Monad
import Data.List
import Data.Bits
import Debug.Trace
import Data.Maybe
import qualified Data.ByteString.Char8 as C
import Data.Ratio

main :: IO ()
main = do
  [a, b] <- readIntegers
  print $ solve a b

-- a + 1

solve a b = if mina <= x && x <= maxa && minb <= x && x <= maxb
  then x
  else
    if mina <= y && y <= maxa && minb <= y && y <= maxb
      then y
      else -1
  where
    x = min mina minb
    y = max mina minb
    mina = ceiling $ fromRational $ (a % 1) * (100 % 8)
    maxa = (ceiling $ fromRational $ ((a + 1) % 1) * (100 % 8)) - 1
    minb = ceiling $ fromRational $ (b % 1) * (100 % 10)
    maxb = (ceiling $ fromRational $ ((b + 1) % 1) * (100 % 10)) - 1

-- 以下ライブラリ

readInts :: IO [Int]
readInts = map (fst . fromJust . C.readInt) . C.words <$> C.getLine

readNInts :: Int -> IO [[Int]]
readNInts = flip replicateM readInts

readIntegers :: IO [Integer]
readIntegers = map (fst . fromJust . C.readInteger) . C.words <$> C.getLine

readNIntegers :: Int -> IO [[Integer]]
readNIntegers = flip replicateM readIntegers

getNLns :: Int -> IO [String]
getNLns = flip replicateM getLine