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 sys import stdin,stdout
def main():
	n,k=map(int,stdin.readline().split( ))
	s=stdin.readline()
	start=-1
	i=0;j=1;prev=1
	while i<n-1:
		while j<n:
			if s[i]==s[j]:
				if start==-1:
					start=j
					prev=j
				i+=1
				j+=1
			else:
				i=0
				j=prev+1
				prev=j
				start=-1
		break
	if start==-1:
		stdout.write("%s\n"%(s[:n]*k))
	else:
		j = n - start
		stdout.write("%s\n"%(s[:n]+s[j:n]*(k-1)))
main()