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 sys
input=sys.stdin.readline
def read():return list(map(int,input().split()))
n,k=read()
s=input()[:-1]
ans=""
for i in range(len(s)+1, 0, -1):
    res=s
    end=s[-i:]
    for j in range(k-1):
        res += end
    cnt=0
    for j in range(len(res)-len(s)+1):
        if res[j:j+len(s)] == s:
            cnt += 1
    if cnt == k:
        ans = res
print(ans)