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, k = map(int, input().split())
s = input()
if (n == 1):
    print(s * k)
    exit()

st = s[:]
cnt = 1
left = 0
flag = False
while (cnt < k):
    flag = False
    for i in range(len(st)):
        if (st[i:] == s[0:len(st) - i] and s[len(st) - i:]):
            left = len(st)
            st += s[len(st) - i:]
            cnt += 1
            flag = True
            break
    #print(cnt, st, flag)
    if (flag == False):
        st += s
        cnt += 1
#print(cnt)
cnt = 0
for i in range(len(st)):
    if (st[i:i + n] == s):
        cnt += 1
    if (cnt == k):
        st = st[:i + n]
#print(cnt)
print(st)