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

result = t * k

for l in range(1, n):
    ss = t[:l]
    if n % l == 0:
        if ss * (n // l) == t:
            c = t + ss * (k - 1)
            if len(c) < len(result):
                result = c
    r = t[-l:]
    if ss == r:
        m = t[l: -l] if l * 2 < n else ""
        r = r if l * 2 < n else t[l:]
        c = t + (m + r) * (k - 1)
        if len(c) < len(result):
            result = c

print(result)