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 = map(int,input().split())
t = input()
i = n - 1
f = True
while f and i > 0:
	if t[len(t) - i:len(t)] == t[:i]:
		f = False
	i -= 1
s = ''
i += 1
if i == 1 and f:
	for i in range(k):
		s += t
	print(s)
else:
	print(t,end = '')
	for j in range(k - 1):
		s += t[i:]
	print(s)