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 problem(in1, in2):
    inputs = list(map(int, in1.split()))
    n = inputs[0]
    k = inputs[1]

    s = in2

    skip = n - 1

    while (skip >= 0):
        end = s[skip:]
        ss = s[-skip:] + end
        if (ss == s):
            break
        skip -= 1


    return s + end * (k - 1)

if __name__ == '__main__':
    in1 = input()
    in2 = input()

    result = problem(in1, in2)
    
    print(result)