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:
def duble(n, t, k):
    if n == 1:
        return t * k
    prefix_dict = {}
    sufix_dict = {}
    for j in range(1, len(t) + 1):
        prefix = t[:j]
        prefix_dict[prefix] = len(prefix)
    for j in range(1, len(t)):
        sufix = t[j:]
        sufix_dict[sufix] = len(sufix)
    s = prefix_dict.keys() & sufix_dict.keys()
    if not s:
        return t * k
    z = list()
    for elem in s:
        z.append(elem)
    return t + t[len(max(z)):] * (k - 1)


N, K = [int(i) for i in input().split()]
s = input()
print(duble(N, s, K))