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())
s,s1=input(),''
c=1
min=99999
d=set(s)
if len(d)==1:
    print(s+s[0]*(k-1))
    exit()
while (c<len(s)):
    if s[:c]==s[len(s)-c:]:
        if min>len(s[:c]+s[c:]*k):
            min=len(s[:c]+s[c:]*k)
            s1=(s[:c]+s[c:]*k)
    c+=1
if s1!='':
    print(s1)
else:
    print(s*k)