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 = map(int, input().split())
t = input()
ans = t
pos = 1
cnt = 1
while cnt < k:
    if pos >= len(ans):
        ans += t
        cnt += 1
    else:
        i = 0
        ok = 1
        while ((pos + i) != len(ans)) and ok == 1:
            if (ans[pos + i] == t[i]):
                i += 1
            else:
                ok = 0
        if ok == 1:
            ans += t[i:]
            cnt += 1
    pos += 1
print(ans)