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()

prefix = ""
suffix = s

for i in range(1, n):
    cur = s[0:i]
    cur_suffix = s[i:]
    flag = 1
    for j in range(i):
        if cur[j] == s[n - i + j]:
            continue
        else:
            flag = 0
            break
    if flag == 1:
        prefix = cur
        suffix = cur_suffix

ret = prefix
for i in range(k):
    ret += suffix
print(ret)