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=str(input())
ss=list(s)
t=""
tt=[]
x=[]
if n==1:
    print(s*k)
    exit()
for i in range(n-1,-1,-1):
    for j in range(i):
        t+=ss[j]
    if s.endswith(t):
        x=True
        break
    t=""
z=""
qqq=""
if x:
    tt=ss[len(t):]
    for i in range(len(tt)):
        qqq+=tt[i]
    z=s+qqq*(k-1)
    print(z)
else:
    print(s*k)