You are given a lowercase string s and an integer k. Repeatedly perform the following operation: choose any block of exactly k consecutive characters that are all equal and delete it. After a deletion the two sides of the string join together, which may create new blocks of k equal characters. Keep applying the operation until no block of k equal adjacent characters remains.
The final string is unique and does not depend on the order in which the deletions are performed. Print that final string.
Input format
Line 1: two space-separated integers n and k, where n is the length of s.
Line 2: the string s of exactly n lowercase English letters. When n is 0 this line is present but empty.
Output format
The final string after all possible deletions. If the final string is empty, print the single word EMPTY instead.
Constraints
- 0 ≤ n ≤ 100000
- 2 ≤ k ≤ 100000
sconsists of lowercase English letters only.