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:
n,k=input().strip().split(' ')
n,k=int(n),int(k)
t=input()
arr=[]
s=''
for i in t:
    s+=i
    arr.append(s)
s=''
cnt=1
s=t
while(cnt<k):
    j=len(s)-n+1
    while(j<len(s) and s[j:] not in arr):
        j+=1
    if(j==len(s)):
        i=-1
    else:
        i=arr.index(s[j:])
    s+=t[i+1:]
    cnt+=1
print(s)