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 prefix_func(s):
    slen, k = len(s), 0
    p = [0]*slen
    p[0] = 0
    for i in range(1, slen):
        while k>0 and s[k] != s[i]:
            k = p[k-1]
        if s[k] == s[i]:
            k += 1
        p[i] = k
    return p

n,k = map(int, input().split())
t = input()
l = 0
p = prefix_func(t)
zm = p[-1]
s = t
for i in range(k-1):
    s += t[zm:]
print(s)