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 = map(int, input().split())
s = input()


def solve():
    global n, k, s
    ans = []
    for i in range(n):
        if s.startswith(s[:i]) and s.endswith(s[:i]):
            ans.append(s[:i])
    ans.sort(key = lambda i : len(i), reverse = 1)
    need = ans[0]
    delete = len(need)
    do = s
    k -= 1
    for i in range(n):
        if s[:i] == need:
            break
    add = s[i:]
    for i in range(k):
        do += add
    print(do)


solve()