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()

pos = 0
if n == 1:
    print(s*k)
    exit()
flag = True
for i in range(n - 1):
    if s[i] != s[i + 1]:
        flag = False
if flag:
    print(s + s[1] * (k - 1))
    exit()

for i in range(n - 1):
    if s[-i - 1:] == s[:i + 1]:
        # print(s[-i - 1:], s[:i + 1])
        # print(i)
        pos = i + 1

# if pos == 0:
#     print(s * k)
#     exit()
#
# print(pos)
print(s + s[pos:]*(k - 1))