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 qualified Data.ByteString.Char8 as B
import qualified Data.Vector as V
import qualified Data.Vector.Unboxed as UV

main=B.interact $ B.pack.g.take 2.B.lines
g [!s,!t]=mk "" (ls-1) (lt-1) where
    ls = B.length s
    lt = B.length t
    rd si ti = (aa V.! si) UV.! ti
    mk !as si ti
        | si<0 || ti<0 = as
        | B.index s si == B.index t ti = mk (B.index s si : as) (si-1) (ti-1)
        | rd (si+1) ti > rd si (ti+1) = mk as si (ti-1)
        | otherwise = mk as (si-1) ti
    aa :: V.Vector (UV.Vector Int)
    aa = V.scanl' p (UV.replicate (lt+1) 0) $ V.enumFromTo 1 ls where
        p v0 i = UV.scanl' m 0 $ UV.enumFromTo 1 lt where
            m pj j = if B.index s (i-1) == B.index t (j-1)
                then 1 + v0 UV.! (j-1)
                else max pj $ v0 UV.! j