Problem:
Score : 100 points

Problem Statement

You are given strings s and t.
Find one longest string that is a subsequence of both s and t.

Notes

A subsequence of a string x is the string obtained by removing zero or more characters from x and concatenating the remaining characters without changing the order.

Constraints

s and t are strings consisting of lowercase English letters.

1 \leq |s|, |t| \leq 3000

Input

Input is given from Standard Input in the following format:

s
t

Output

Print one longest string that is a subsequence of both s and t.
If there are multiple such strings, any of them will be accepted.

Sample Input 1

axyb
abyxb

Sample Output 1

axb

The answer is axb or ayb; either will be accepted.

Sample Input 2

aa
xayaz

Sample Output 2

aa

Sample Input 3

a
z

Sample Output 3

The answer is (an empty string).

Sample Input 4

abracadabra
avadakedavra

Sample Output 4

aaadara

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

{-# LANGUAGE BangPatterns #-}
import Control.Monad
import Data.Word
import qualified Data.ByteString as BSW
import qualified Data.ByteString.Char8 as BS
import Data.Array.Unboxed
import Data.Array.ST

-- Input: s t
-- Output: arr
--   arr ! (i,j) == length of lcs of (drop i s, drop j t)
lcsTable2 :: BS.ByteString -> BS.ByteString -> UArray (Int,Int) Word16
lcsTable2 s t = runSTUArray $ do
  let !m = BS.length s
      !n = BS.length t
      !n' = n+1
  arr <- newArray ((0,0),(m,n)) 0
  forM_ [m-1,m-2..0] $ \ !i -> do
    let !x = BSW.index s i
        loopY !j !v
          -- v = readArray arr (i,j+1)
          | j < 0 = return ()
          | otherwise = do
              let !y = BSW.index t j
              if x == y
                then do l2 <- readArray arr (i+1,j+1)
                        let !l = l2 + 1
                        writeArray arr (i,j) l
                        loopY (j-1) l
                else do l0 <- readArray arr (i+1,j)
                        let !l = max l0 v
                        writeArray arr (i,j) l
                        loopY (j-1) l
    loopY (n-1) 0
  return arr

main = do
  s <- BS.getLine
  t <- BS.getLine
  -- BS.length s <= 3000, BS.length t <= 3000, BS.all isAsciiLower s, BS.all isAsciiLower t
  let !table = lcsTable2 s t
      !m = BS.length s
      !n = BS.length t
      !n' = n+1
  let recon !i !j | i >= m || j >= n = Nothing
                  | x == y = let !i' = i+1 ; !j' = j+1
                             in Just (x, (i', j'))
                  | table ! (i+1,j) >= table ! (i,j+1) = recon (i+1) j
                  | otherwise = recon i (j+1)
        where x = BSW.index s i
              y = BSW.index t j
      (result, _) = BSW.unfoldrN (fromIntegral $ table ! (0,0)) (\(!i,!j) -> recon i j) (0,0)
  BS.putStrLn result