Ivana made up a long word of N letters. Then she wrote down all K-letter-substrings of that word. For example, if the original word is BANANA and K=3, Ivana writes down the words BAN, ANA, NAN, ANA. The number of these words is, obviously, N-K+1.

Ivana sorted these words in lexicographic order (in the given example, that would be ANA, ANA, BAN, NAN).

But the sad thing happened: Ivana forgot the original word! Your task is to reconstruct it. A unique solution will exist in all of the test data.

Constraints: 3 ≤ N ≤ 100 000, 2 ≤ K ≤ 15, K < N.

Input

[integers N, K]

[N-K+1 words in lexicographic order, each consisting of capital English letters]

Output

[the required word]

Example

Input:
6 3
ANA
ANA
BAN
NAN

Output:
BANANA