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())
arr=[0 for i in range(n)]
s=input()
s1=s
count=0
j=0

for i in range(1,n):
            j=arr[i-1]           
            while j>0 and s[i]!=s[j]:
                j=arr[j-1]
            
            if s[i]==s[j]:
                j=j+1

            arr[i]=j   

len=n-arr[n-1]
#print(s[0:len])
print(s[0:len]*(k-1)+s)