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:
def p(t,n):
   out=0
   if n==1:
      return(0)
   for i in range(1,n):
      t1=t[:i]
      t2=t[n-i:]
      if t1==t2:
         out=max([out,len(t1)])
   return(out)

inp=input("").split()
n=int(inp[0])
k=int(inp[1])
t=input("")
x=p(t,n)
ans=t+(t[x:]*(k-1))
print(ans)