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:
#!/usr/bin/python3

n, k = [int(x) for x in input().split()]

t = input()
max_prefix = ''

for i in range(1, len(t)):
    l = t[-i:]
    # print(str(i) + " : " + l)
    if(t.startswith(l)):
        max_prefix = l

# print("Max prefix :- " + max_prefix)

s = ''

if len(max_prefix) == 0:
    for i in range(k):
        s = s + t
else:
    p = t[:n-len(max_prefix)]
    for i in range(k-1):
        s = s + p
    s = s + t

print(s)