Problem Statement

Iroha has a sequence of $N$ strings $s_1, s_2, ..., s_N$.

She will choose some (possibly all) strings from the sequence, then concatenate those strings retaining the relative order, to produce a long string.

Among all strings of length $K$ that she can produce in this way, find the lexicographically smallest one.

Constraints

• $1 ≦ N ≦ 2000$
• $1 ≦ K ≦ 10^4$
• For each $i$, $1 ≦ |s_i| ≦ K$.
• $|s_1| + |s_2| + ... + |s_N| ≦ 10^6$
• For each $i$, $s_i$ consists of lowercase letters.
• There exists at least one string of length $K$ that Iroha can produce.

Input

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

N K
s_1
s_2
:
s_N

Output

Print the lexicographically smallest string of length $K$ that Iroha can produce.