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 PYTHON):

Solution:
import sys

def test():
    global t
    global s
    global k
    global n

    co = 0
    for i in range(len(s)):
        t1 = s[i:i+n]
        if t1 == t:
            co +=1

    if co == k:
        return True
    return False

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

t = raw_input()
n = len(t)

_t = ''

for i in range(1, n+1):
    s1 = t[i:]
    s2 = t[:n-i]
    if s1 == s2:
        break

_t = t[n-i:]



    
s = t

for i in range(k-1):
    s += _t

assert test()

print s