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:
# http://codeforces.com/contest/1029/problem/A

n, k = [int(i) for i in input().split(" ")]
word = input()

s = 0
for i in range(1, n):
    if word[:i] == word[-i:]:
        s = i

prefix = word[:-s] if s > 0 else word
suffix = word[-s:] if s > 0 else ""

ans = ""
for i in range(k):
    ans += prefix
ans += suffix

print(ans)