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():
    n, k = map(int, input().split())
    t = input()

    def prefix_function(s):
        n = len(s)
        F = [0] * n
        for i in range(1, n):
            j = F[i-1]
            while j > 0 and s[i] != s[j]:
                j = F[j-1]
            if s[i] == s[j]:
                j += 1
            F[i] = j
        return F

    print(t[:n-prefix_function(t)[n-1]] * (k-1) + t)


if __name__ == '__main__':
    main()