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:
t,k=map(int,input().split())
string_=input()
for i in range(1,t+1):
    ge=t//i
    if string_[:i]*ge==string_[:i*ge] and (string_[i*ge:]=='' or string_[i*ge:]==string_[:t-i*ge]):
        zhouqi=i
        break
output=''
for r in range(k-1):
    output+=string_[:zhouqi]
output+=string_
print(output)