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 = input().split(" ")

    n = int(n)
    k = int(k)
    t = input() # the string t

    cnt = 1
    ans = t
    pos = 1

    while cnt < k:

        if (pos >= len(ans)):
            ans += t
            cnt += 1
            pos += 1

        else:
            if (t.startswith(ans[pos:])):
                prefix_len = len(ans[pos:])
                ans += t[prefix_len:]
                cnt += 1
                pos += 1

            else:
                pos += 1

    print(ans)

    # # print the string s of minimum possible length that there are exactly k substrings of s equal to t
    # if (len(t) > 1):
    #     s = [c for c in t*k]
    #     skip_list = []

    #     for i in range(0, n*(k-1), n):
    #         if (s[i+n-1] == s[i+n]):
    #             skip_list.append(i+n-1)

    #     result = ""

    #     for i in range(n*k):
    #         if (i not in skip_list):
    #             result += s[int(i)]

    #     print(result)

    # else:
    #     # if length is 1 simply print it
    #     print(t)

if __name__ == "__main__":
    main()