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:
from math import ceil
n,k = map(int,input().split())
s = input()
d = ""
for i in range(n-1):
	# print(s[:i+1], s[n-i-1:n],s[:i+1] == s[n-i-1:n] ,s[i+1:n])
	if(s[:i+1] == s[n-i-1:n]):
		d = s[i+1:n]
if d == "":
	d = s
print(s,end="")
for i in range(1,k):
	print(d,end="")