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=list(input())

a=done=i=b=total=c=0
while i<n:
    if i!=0:
       if done==0:
          if s[i]==s[0]:
             a+=1
             done=1
          i+=1   
       else:
          if s[i]==s[a]:
             a+=1
             if c==0:
                if s[i]==s[0]:
                   total=1
                   b=i
                   c+=1
             i+=1       

          else:
             if total==1:
                i=b
                c=0
                total=0

             a=0
             done=0
    
    else:
        i+=1         


l=''
count=0
y=n-a
x=y*k
i=0
while count!=x:
    if i==y:
       i=0
    l+=s[i]
    i+=1
    count+=1

for i in range(a):
    l+=s[i]

print(l)