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=list(map(int,input().split()))
t=input()
start=0
end=1
length=0
while(end<n):
    if(t[start]==t[end]):
        i=start
        j=end
        while(j<n):
            if(t[i]==t[j]):
                i+=1
                j+=1
            else:
                break
        if j==n and n-end>length:
            length=n-end
    end+=1
res=t
while(k-1!=0):
    res=res+t[length:]
    k-=1
print(res)