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.

axyb
abyxb

axb

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

aa
xayaz

aa

a
z

The answer is `` (an empty string).

abracadabra
avadakedavra

aaadara