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(' '))
t = input()

s = set()
for c in t:
    s.add(c)
if len(s) == 1:
    print(t, end='')
    for i in range(k-1):
        print(t[0], end='')
    print('')
else:
    # Get the longest prefix that is also suffix
    suffixsize = 0
    for i in range(n - 1, 0, -1):
        if t[:i] == t[-i:]:
            suffixsize = i
            break
    if suffixsize > 0:
        print(t, end='')
        for i in range(k - 1):
            print(t[-(n-suffixsize):], end='')
        print('')
    else:
        for i in range(k):
            print(t, end='')
        print('')