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:
import io
import os
#input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline


def main():
    n, k = map(int, input().split())
    t = input()

    def checkPrefix(len):
        L=0
        R=len
        while R < n:
            if t[L] != t[R]:
                return False
            L += 1
            R += 1
        return True

    if n == 1:
        print(t * k)
    else:
        prefix_len = 1
        while not checkPrefix(prefix_len):
            prefix_len += 1

        print(t[:prefix_len] * (k-1) + t)

    prefix_len = 0



if __name__ == '__main__':
    main()