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(" "))
k_ = k
t = input().strip()
l = len(t)
#print(n,k)
#print(t)

s = t
k -= 1
repeats = False

while (k != 0):
  for i in range(l-1, 0, -1):
    if (s[:i]==s[-1*i:]):
      s += t[i:]
      k -= 1
      repeats = True
      #print(s)
      break
  if not repeats:
    s = t*k_
    break

print(s)