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:
import sys

n, k = map(int, sys.stdin.readline().split())
t = sys.stdin.readline().strip()

c = 0
if len(t)>1:
    for i in range(1, len(t)):
        while t[0 + c] == t[i+ c]:
            c+=1
            if i+c == len(t):
                break
        if i+c==len(t):
            break
        else:
            c = 0
        

sys.stdout.write(t)
for _ in range(k - 1):
	sys.stdout.write(t[c:])