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
def longestPrefixSuffix(s,s1) : 
    n = s1 
    if(n < 2):
        return 0
    le = 0 
    i = n//2    
    while(i < n) :
        if(s[i]==s[le]):
            le+=1
            i+=1 
        else:
            if(le == 0): 
                i+=1
            else:
                le-=1
    return le


n=input().split(" ")
k=input()
ans=k
end=0
for i in range(1,len(k)):
    if(k[:i]==k[len(k)-i:]):
        end=i
for i in range(int(n[1])-1):
    ans+=k[end:]
print(ans)