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:
def fun(s,t):
    ns=len(s)
    ma=-1
    for i in range(len(t)):
        if(s[ns-i:]==t[:i]):
            ma=i
    #print ma
    if ma<=0:
        return s+t
    else:
        return s+t[ma:]
n,m=[int(i) for i in raw_input().split()]
t=raw_input()
res=t
for i in range(m-1):
    res=fun(res,t)
print res