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=input(); r=n
for i in range(1,n):
    r1=n-i
    if s[:r1]==s[i:]: r=i; break
cnt=s.count(s[r:])
# print(cnt,s[r:],r)
if cnt>1 and cnt*len(s[r:])==n:
    print(s,end="")
    print(s[r:]*(k-1))
else: print(s[:r]*k+s[r:])