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 solve():
    n, k = map(int, input().split())
    t = input()
    if n == 1 or k == 1:
        print(t * k)
        return
    for i in range(1, n):
        if n % i == 0:
            c = t[:i]
            if c * (n // i) == t:
                print(c * (n // i + (k - 1)))
                return
    s = t
    h = n // 2
    for i in range(n):
        if n % 2 == 1:
            if s[:h - i + 1] == s[h + i:]:
                s = s[h - i + 1:]
                break
        else:
            if s[:h - i] == s[h + i:]:
                s = s[h - i:]
                break
    print(t + (s * (k - 1)))


if __name__ == '__main__':
    solve()