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 PYTHON):

Solution:
#coding:utf-8
tmp = raw_input().split()
n = int(tmp[0])
k = int(tmp[1])
t = raw_input()
if len(set(t)) == 1:
	print(t[0]*(n-1+k))
	exit()
idx = 0
flag = False
for i in range(n-1):
	# print(i)
	# print(t[0:i+1],t[n-1-i:])
	if t[0:i+1] == t[n-1-i:]:
		idx = i
		flag = True

if flag ==True:
	print((k-1)*t[:n-idx-1]+t)
else:
	print(t*k)