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 math import ceil

def prefix_function(s, n):
    for i in range(0, n - 1):
        s1 = s[0:i + 1]
        s2 = s1 * ceil(n / len(s1))
        try:
            if s2.index(s) == 0:
                return s1
        except:
            pass
    return s #Здесь пишет "IndentationError" - unexpected unident, на этой строке

n, k = [int(x) for x in input().split()]
t = input()

p = prefix_function(t, n)

print(p * (k - 1), t, sep = '')