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:
parameters = list(map(int, input().split(' ')))
s = str(input())
n = parameters[0]
k = parameters[1]
import math


def findMaxDuplicatedSubStringLength(s):
    last_char = s[len(s) - 1]
    result = 0
    continue_looping = True
    subStringLength = math.ceil((len(s)/2))
    while continue_looping:
        beginnigSubString = s[:subStringLength]
        last_index = beginnigSubString.rfind(last_char)
        if(last_index == -1):
            continue_looping = False
        else:
            beginnigSubString = s[:last_index+1]
            endingSubstring = s[len(s) - last_index - 1:]
            if(endingSubstring == beginnigSubString):
                continue_looping = False
                result = last_index + 1
            subStringLength = last_index

    return result


def findMinDuplicatedSubStringLength(s):
    subStringLength = 1
    continue_looping = True
    result = len(s)
    while(continue_looping and subStringLength <= math.ceil((len(s)/2))):
        subString = s[: subStringLength]
        if(s == subString * int(len(s) / len(subString))):
            result = len(subString)
            continue_looping = False
        subStringLength += 1
    return result


def returnResult(s, k):
    result = s
    if(len(s) == 1):
        for k in range(k-1):
            result = result + s
        print(result)
        return
    stringToDuplicate = ''
    finalDuplicateSubStringLength = findMaxDuplicatedSubStringLength(s)
    stringToDuplicate = s[finalDuplicateSubStringLength:]
    if(findMinDuplicatedSubStringLength(s) < len(s)):
        stringToDuplicate = s[:findMinDuplicatedSubStringLength(s)]
        for i in range(k-1):
            result = result + stringToDuplicate
    else:
        for i in range(k-1):
            result = result + stringToDuplicate

    print(result)


returnResult(s, k)