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()
p = [0] * len(s)

for i in range(1, len(s)):
    p[i] = p[i - 1]
    while p[i] > 0 and s[p[i]] != s[i]:
        p[i] = p[p[i] - 1]
    if s[p[i]] == s[i]:
        p[i] += 1

print(s, end = '')
for i in range(1, k):
    for j in range(p[-1], len(s)):
        print(s[j], end='')
print()