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:
# -*- coding: utf-8 -*-


def get_next(t, nxt):
    t = ' ' + t
    i = 1
    j = 0
    nxt[1] = 0
    m = len(t) - 1
    while i < m:
        if j == 0 or t[i] == t[j]:
            i += 1
            j += 1
            nxt[i] = j
        else:
            j = nxt[j]
    return nxt[m]


n, k = map(int, input().split())
t = str(input())
nxt = [0] * (len(t) + 1)
length = get_next(t, nxt)
if t[length - 1] != t[-1]:
    if t[0] == t[-1]:
        length = 1
    else:
        length = 0
print(t[0:n - length] * k + t[n - length:n])