Problem:
Score : 300 points

Problem Statement

Snuke loves puzzles.

Today, he is working on a puzzle using S- and c-shaped pieces.
In this puzzle, you can combine two c-shaped pieces into one S-shaped piece, as shown in the figure below:

Snuke decided to create as many Scc groups as possible by putting together one S-shaped piece and two c-shaped pieces.

Find the maximum number of Scc groups that can be created when Snuke has N S-shaped pieces and M c-shaped pieces.

Constraints

1 ≤ N,M ≤ 10^{12}

Input

The input is given from Standard Input in the following format:

N M

Output

Print the answer.

Sample Input 1

1 6

Sample Output 1

2

Two Scc groups can be created as follows:

Combine two c-shaped pieces into one S-shaped piece

Create two Scc groups, each from one S-shaped piece and two c-shaped pieces

Sample Input 2

12345 678901

Sample Output 2

175897

Solution in Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import Control.Monad
import Data.Maybe
import qualified Data.ByteString.Char8 as C

solve m n acc
  | m /= 0 && n >= 2 = solve (m - 1) (n - 2) (acc + 1)
  | n >= 4 = solve m (n - 4) (acc + 1)
  | otherwise = acc

  
main = do
  [m, n] <- readInts
  -- print $ solve 1 6 0
  -- print $ solve 12345 678901 0
  print $ solve m n 0
  where
    toInt :: String -> Int
    toInt = read

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