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:
def next(s1,s2):
	n = len(s1)
	m = len(s2)
	i = 1
	while (i != m):
		# print('s1 =',s1[(n-m + i):] ,'s2 =', s2[:m-i ])
		if (s1[(n-m + i):] == s2[:m-i ]):
			# print("HERE")
			return s1 + s2[m-i: ]
		i += 1
	return s1 + s2


a, b = (int(i) for i in input().split())
s = input()
result = s
for i in range(b-1):
	result = next(result, s)
print(result)