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, math
from sys import stdin, stdout
rem = 10 ** 9 + 7
sys.setrecursionlimit(10 ** 6+5)
#from resource import *; setrlimit(RLIMIT_STACK, (RLIM_INFINITY, RLIM_INFINITY))
take = lambda: map(int, stdin.readline().split())

def help(a,b):
    n=len(a)
    m=len(b)
    cnt=0
    for i in range(n-m+1):
        if a[i:i+m]==b:
            cnt+=1
    #print a,b,cnt
    return cnt


n,k=take()
s=list(raw_input())

prev=[]
for i in range(1,n+1):
    now=s+prev*(k-1)
    if help(now,s)==k:
        print ''.join(now)
        exit()
    prev=[s[-i]]+prev
    now = s + prev * (k - 1)
    if help(now, s) == k:
        print ''.join(now)
        exit()