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 mi():
	return map(int, input().split())

n,k = mi()
s = list(input())

comm=0
for i in range(n):
	for j in range(n):
		if s[:i]==s[j:]:
			comm=i
t = s[:n-comm]
t*=1000
stop = -1
c = 0
for i in range(len(t)):
	if t[i:i+n]==s:
		c+=1
	if c==k:
		stop = i
		break
t = t[:stop+n]
print (''.join(t))