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()
s=t
f=1
if t[0]*n==t:
    print(t+(k-1)*t[0])
else:
    for i in range(1,n):
        if t[i]==t[0]:
            break
    while i<=len(t)-1:
        if t[i:]==t[:n-i]:
            f=0
            break
        else:
            i+=1
    if f==1:
        print(k*t)
    else:
        j=n-i
        s+=(k-1)*t[j:]
        print(s)