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:
# PREFUNCS
def inline():
    return [ int(n) for n in input().split() ]



# INPUT
lst = inline()
l = lst[0]
n = lst[1]
s = input()



# PROCESS
same = 0
for i in range(l - 1, 0, -1):
    # beginnign == ending
    if s[:i] == s[-i:]: 
        same = i
        break

diff = s[-l + same:]
for j in range(n - 1): s += diff



# OUTPUT
print(s)