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())
t = input()

for i in range(1,len(t)+1):

    if len(t) % i != 0:
        continue

    substr = t[:i]
    times = int(len(t) / i)
    
    ist = substr*times 
    if ist == t:
        break 
if 1<len(ist):
    for i in range(len(ist)-1,0,-1):
        if ist[len(ist)-i : len(ist)] == ist[0 : i]:
            ist = ist[0:len(ist)-i]
            break
         
        
print(ist*(k-1) + t)