Problem: You are given a string t consisting of n lowercase Latin letters and an integer number k.

Let's define a substring of some string s with indices from l to r as s[l ... r].

Your task is to construct such string s of minimum possible length that there are exactly k positions i such that s[i ... i + n - 1] = t. In other words, your task is to construct such string s of minimum possible length that there are exactly k substrings of s equal to t.

It is guaranteed that the answer is always unique.

Input

The first line of the input contains two integers n and k (1 ≤ n, k ≤ 50) — the length of the string t and the number of substrings.

The second line of the input contains the string t consisting of exactly n lowercase Latin letters.

Output

Print such string s of minimum possible length that there are exactly k substrings of s equal to t.

It is guaranteed that the answer is always unique.

Examples

Input

3 4
aba


Output

ababababa


Input

3 2
cat


Output

catcat

Solution (in PYTHON3):

Solution:
n, k = input().split(' ')
n = int(n)
k = int(k)
s = input()
i = 1
while s[i:] != s[:-i]:  # gonna find the first case which a pallindrome is found.
	i = i + 1			# This make s[:i] be the string with minimum possible length
						# so that, when repeate but shares the char in the middle, 
						# the case s[i] == s[i + n - 1] occurs
print(s[:i]*k + s[i:])
# The [:i] discards the right border of the string starting at the left,
# so that a copy can be joined to the right without losing space by
# repeating the character at position s[i] which is common to both strings.
# And finally, the last string added must be the entire s[i:]  because there's
# no other string to be placed after it.