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:
def prefix(s):
    v = [0] * len(s)
    for i in range(1,len(s)):
        k = v[i-1]
        while k>0 and s[k] != s[i]:
            k = v[k-1]
        if s[k] == s[i]:
            k += 1
        v[i] = k
    return v


s = input()
n,k = s.split(' ')
n= int(n)
k = int(k)
s = input()


pi = prefix(s)

l = len(s) - pi[n-1]

i=0
while i<k-1:
    print(s[:l],end = '')
    i += 1
print(s)