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:
# only gravity will pull me down

from math import *

n, k = map(int, input().split())
t = input()

if len(set(t)) == 1 :
	res = t + t[0] * (k-1)
	#print(res)

elif t == t[::-1] :
	ch = t[0]
	cnt = 0
	for i in t :
		if i == ch :
			cnt += 1
		else :
			break
	res = t + t[cnt:] * (k-1)
	#print(res)
else :
	res = t * k

x = n-1
while t[:x] != t[n-x:] :
	x -= 1
res1 = t + t[x:] * (k-1) 
	#print(res)
if len(res) > len(res1) :
	print(res1)
else :
	print(res)