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:
def subs(s, d):
    for k in range(len(s) - d):
        if s[k] != s[k + d]:
            return False
    return True

def pallen(s):
    for d in range(1, len(s)):
        f = subs(s, d)
        if f:
            return d
    return 0

n, k = map(int, input().split())
s = input()
i = pallen(s)
if i == 0:
    for _ in range(k):
        print(s, end="")
    print()
else:
    for _ in range(k):
        print(s[:i], end="")
    print(s[i:])
#
# tests = [
#     ("aba", 2),
#     ("cat", 0),
#     ("aaaa", 1),
#     ("ababab", 2),
#     ("abcdeabc", 5),
#     ("aecnvrlcxdatboldlurjlmmlhuaccmlwkdvkqvzmiazhotdnyp", 0)
# ]
#
# for a, r in tests:
#     o = pallen(a)
#     assert o == r, f"{a}, {o}, {r}"