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:
def eq(s):
    for i in range(1,len(s)):
        if s[:len(s) - i] == s[i:]:
            #print([s[:len(s) - i], s[i:]])
            return s[-1 * i:], s[i:]
    
    return '', s

n, k = map(int, input().split(' '))
s = input()

t, s = eq(s)
#print([t,s])

if t == '':
    t = s * (k - 1)
else:
    t = t * k

print(s + t)