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 getNext(pattern):
    next1 = []
    j = 0
    plen = len(pattern)
    next1.append(0)
    for i in range(1, plen):
        while j > 0 and pattern[j] != pattern[i]:
            j = next1[j-1]
        if pattern[i] == pattern[j]:
            j = j + 1
        next1.append(j)
    return next1
m, s = list(map(int, input().split()))
l = input()
n = getNext(l)[-1]
print(l + l[n:] * (s-1))