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, t = map(int, input().split())
s = input()
k = 0
prRes = []
for i in s:
    prRes.append(0)
k = 0
for i in range(1, len(prRes)):
    while ((k > 0) and (s[k] != s[i])):
        k = prRes[k-1]
    if (s[k] == s[i]):
        k += 1
    prRes[i] = k
if (n == 1) or (prRes[len(prRes) - 1] == 0):
    print(s * t)
else:
    cycle = s[:len(s) - prRes[len(prRes) - 1]]
    print(cycle * (t - 1) + s)