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 main():
    input1 = input()
    s = input()
    input1 = input1.split(' ')
    n = int(input1[0])
    k = int(input1[1])
    j = 0
    for i in range(n - 1):
        if s[:(i+1)] == s[-(i + 1):]:
            if i + 1 > j:
                j = i + 1

    sub = s[j:]
    print(s + ''.join([sub] * (k-1)))


if __name__ == '__main__':
    main()