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:
from sys import stdin
lines = stdin.readlines()


n,k = map(int,lines[0].split())
temp = k
t = lines[1][:-1]
k -= 1
result = t
while k>0:
    c = len(result)
    flag = True
    for i in range(c-n+1,c):
        c2 = result[i:]
        if t[:c-i] == c2:
            result += t[c-i:]
            flag = False
            break
    if flag:
        result += t
    k -= 1
if n == 1:
    print t*temp
else:
    print result