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:
n, k = (int(i) for i in input().split())

substr = input()
answer = substr

if n == 1:
    print(substr * k)
else:

    for i in range(k - 1):
        start = len(answer) - n + 1
        end = n - 1
        for j in range(n - 1):
            if answer[start:].find(substr[:end]) != -1:
                answer += substr[end:]
                break
            elif end == 1:
                answer += substr
            start += 1
            end -= 1

    print(answer)