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:
length_t, num_sub_strings = map(int, input().split())
t = input()
repeat = length_t
for pos in range(1, length_t):
    if t[pos:] == t[:length_t - pos]:
        repeat = pos
        break
if repeat == length_t:
    print(''.join([t]*num_sub_strings))
else:
    solution = [t]
    suffix = t[-repeat:]
    solution.extend(suffix*(num_sub_strings - 1))
    print(''.join(solution))