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:
def connection(txt1,txt2):
    ref1 = []
    ref2 = []
    for i in range(len(txt1)-1,-1,-1):
        ref1.append(hash(txt1[i:]))
    for j in range(1,len(txt2)+1):
        ref2.append(hash(txt2[0:j]))
    ans = []
    try:
        i = 0
        while True:
            if ref1[i] == ref2[i]:
                ans.append(len(txt1)-i-1)
            i+=1
    except IndexError:
        pass
    ans.sort()
    for item in ans:
        if item != 0:
            return item
    return -1

n,k = map(int,input().split())
txt = input()
ans = connection(txt,txt)
if ans != -1:
    print(txt+txt[len(txt)-ans:]*(k-1))
else:
    print(txt*k)