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())
t = input()
ind = -1
for i in range(n - 1):
    if (t[0:i + 1] == t[n - i - 1::]):
        #print(t[0:i + 1], i)
        ind = i
if ind == n - 1:
    print(t, end="")
    for i in range(k - 1):
        print(t[0], end="")
    exit(0)
ans = t[0:ind + 1:]
l = t[ind + 1::]
while k > 0:
    k -= 1
    ans += l
print(ans)