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:
# 1029A

n, k = [int(num) for num in input().split(' ')]
string = input()


def fn(string, k):
    maximum_match = 0
    for i in range(1, len(string)):
        if string[:i] == string[-i:]:
            maximum_match = i

    answer = list(string)
    extra = list(string[maximum_match:])
    for i in range(k-1):
        answer.extend(extra)

    return ''.join(answer)


print(fn(string, k))