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:
def check(m, idx, orig):
    if m[:orig]==m[len(m)-orig:]:
        return True
    else:
        return False

n,k = [int(i) for i in raw_input().split()]
s = raw_input()
orig = len(s)
for i in range(len(s)-1,-1,-1):
    m = s + s[i:]
    if check(m, i+1, orig)==True:
        print (s[:len(s)-i])*k + s[len(s)-i:]
        break