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




















class KMP (object):
	def __init__ (self):
		self.next = [0 for i in range (55)] #设置数组的大小

	def get_next (self, T): #求得T的next数组
		i = self.next[0] = -1
		j = 0
		T_len = len (T)
		while j < T_len:
			if i < 0 or (T[i] == T[j]): #匹配上了
				i += 1
				j += 1
				self.next[j] = i
			else:
				i = self.next[i]

	def kmp (self, T, P): #进行一次匹配
		pass


a, b = map (int, raw_input ().strip ().split ())
c = raw_input ()
sol = KMP ()
sol.get_next (c)
#print sol.next[:a+1]
for i in range (1, b):
	for j in range (sol.next[a], a):
		c += c[j]
print c