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:
# http://codeforces.com/contest/1029/problem/A
n, k = input().split()
n, k = int(n), int(k)

t = input()
if n == 1:
    ans = t*k
else:
    ans = t
    pos = 1
    cnt = 1
    while cnt < k:
        if pos >= len(ans):
            ans += t
            cnt += 1
        elif t.startswith(ans[pos:]):
            ans += t[len(ans)-pos:]
            cnt += 1
        pos += 1
print(ans)