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:
#!/usr/bin/env python
# -*- coding: utf-8 -*-
n = 0
k = 0

while not ((n>0 and n<=50) and (k>0 and k<=50)):
	try:
		n,k = [int(n) for n in raw_input().split()]
	except ValueError:
		print "Inputs must be an integer!"

t=""
while len(t) != n or any( [i>'z' or i<'a' for i in t] ):
	t = raw_input()


s=False

for i in range(n-1, -1, -1):
	if t[:i] == t[-i:]:
		m = t[i:]
		print t + m*(k-1)
		s=True
		break
if not s:
	print t*k