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:
n, k = map(int, raw_input().strip().split(' '))
t = raw_input().strip()
prefixes = []
for i in range(n - 1):
    prefixes.append(t[0 : i + 1])
suffixes = []
for i in range(n - 1, 0, -1):
    suffixes.append(t[i : ])
pos = None
for i in range(n - 2, -1, -1):
    if (suffixes[i] in prefixes):
        pos = len(suffixes[i])
        break
ans = t
if not(pos is None):
    c = 1
    while c < k:
        ans = ans + t[pos: ]
        c += 1
else:
    c = 1
    while c < k:
        ans = ans + t
        c += 1
print ans