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 math
str1 = input()
n, k = list(map(lambda x: int(x), str1.split(' ')))
t = list(input())

count = -1

for i in range(1, n):
    #print(t[0:i], t[n-i:n])
    if t[0:i] == t[n-i:n]:
        #print(t[0:i], t[n-i:n])
        count = i

#print(count)

mystr = ''

part1 = ''
part2 = ''
for elem in t[0:n-count]:
    part1 += str(elem)

for elem in t[n-count:n]:
    part2 += str(elem)

for i in range(k):
    #print(mystr)
    mystr += part1

mystr += part2
#print(part1)
#print(part2)
print(mystr)