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 PYTHON):

Solution:
n,k=map(int,raw_input().split())
s=raw_input()
lps=[0]*n
l=0
i=1
while i<n:
    if(s[i]==s[l]):
        l+=1
        lps[i]=l
        i+=1
    else:
        if l==0:
            lps[i]=0
            i+=1
        else:
            l=lps[l-1]
t=s[lps[n-1]:]
for i in xrange(k-1):
    s+=t
print s