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:
n, k = input().split()
s = input()
t = ""
counter = int(n)
for i in range(int(n)):
    if s[i] == s[int(n) - 1] and i != int(n) - 1:
        y = int(n) - i - 1
        if s[:i + 1] == s[y:]:
            counter = y
for i2 in range(int(k)):
    if i2 < int(k) - 1:
        t = t + s[:counter:]
    elif i2 == int(k) - 1:
        t = t + s[::]
print(t)