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 = [*map(int, input().split())]
st = input()
ans = st
i = 1
count = 1
while count < k:
    j = 0
    f = False
    if i == len(ans):
        ans += st
        count += 1 
        i += 1
        continue
    while ans[i + j] == st[j]:
        j += 1
        if (i + j) >= len(ans):
            f = True
            break
    if f:
        ans += st[j:]
        count += 1
    i += 1
print(ans)