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())
t = input()
P = [0] * n
for i in range(1, n):
    j = P[i - 1]
    while t[j] != t[i] and j > 0:
        j = P[j - 1]
    if t[i] == t[j]:
        j += 1
    P[i] = j

ans = t[:(n - P[n - 1])] * k
if P[n - 1] > 0:
    ans += t[(n - P[n - 1]):]
print(ans)