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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

s = gets.chomp.chars
t = gets.chomp.chars
n = s.size
m = t.size

dp = Array.new(n+1){Array.new(m+1, 0)}
n.times do |i|
  dp_cur = dp[i]
  dp_next = dp[i+1]
  m.times do |j|
    if s[i] == t[j]
      dp_next[j+1] = dp_cur[j] + 1
    else
      a = dp_cur[j+1]
      b = dp_next[j]
      dp_next[j+1] = a > b ? a : b
    end
  end
end

i, j = n, m
ans = ''
while i > 0 && j > 0 do
  if dp[i][j] == dp[i-1][j]
    i -= 1
  elsif dp[i][j] == dp[i][j-1]
    j -= 1
  else
    ans << s[i-1]
    i -= 1
    j -= 1
  end
end

puts ans.reverse