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(i) for i in input().split()]
t = input()
i = 1
ti = 0
while i != n:
    if t[:i] == t[n - i:]:
        ti = i
    i += 1
s = t[0]
f = 1
for j in t:
    if j != s:
        f = 0
        break
if ti == 0:
    print(t * k)
elif f:
    print(t + (k - 1) * t[-1])
else:
    print(t + t[ti:] * (k - 1))