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 PYTHON):

Solution:
n, k = map(int, raw_input().split())
t = raw_input()
s = t


def f(s, t):
    cnt = 0
    for i in range(len(s)):
        if s[i:i + len(t)] == t:
            cnt += 1
    return cnt


def mat(s, t, cnt):
    return s[len(s) - cnt:] == t[:cnt]


while f(s, t) < k:
    ans = -1
    for cnt in range(n - 1, -1, -1):
        if mat(s, t, cnt):
            ans = cnt
            break
    s += t[ans]
print s