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:
from collections import deque
from sys import stdin
lines = deque(line.strip() for line in stdin.readlines())

def nextline():
    return lines.popleft()

def types(cast, sep=None):
    return tuple(cast(x) for x in strs(sep=sep))

def ints(sep=None):
    return types(int, sep=sep)

def strs(sep=None):
    return tuple(nextline()) if sep == '' else tuple(nextline().split(sep=sep))

def main():
    # lines will now contain all of the input's lines in a list
    _, k = ints()
    s = nextline()
    for i in range(len(s)-1, 0, -1):
        if s.endswith(s[:i]):
            add = s[i:]
            break
    else:
        add = s
    print(s + add * (k - 1))

if __name__ == '__main__':
    main()