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 = list(map(int, input().split()))
t = input()
cnt = 0


for i in range(1, n):
    cnt = 0
    for j in range(n - i):
        if t[j] == t[i + j]:
            cnt += 1
        else:
            break
    if cnt == n - i:
        cnt = i
        break
# if cnt == n //

if cnt == 0:
    print(t * k)
    exit()

f = t[n - cnt:n]
res = t + (k - 1) * f

print(res)