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:
x, y = [int(x) for x in input().split()]
s = input()

if x == 1:
    t = s*y
    print(t)
else:
    count = 0
    t = s
    for i in range(len(s)):
        if s[:i+1] == s[-i-1:]:
            count += 1
            if len(s[:-i-1]) != 0:
                t = s[:-i-1]
            #print(s[:i+1], s[-i-1:], t)
    if count == 0:
        print(s*y)
    else:
        print(t*(y-1)+s)