Kolya and Tandem Repeat

Description:

Input:

The first line contains s (1 ≤ |s| ≤ 200). This string contains only small English letters. The second line contains number k (1 ≤ k ≤ 200) — the number of the added characters.

Output:

Print a single number — the maximum length of the tandem repeat that could have occurred in the new string.

Sample Input:

aaba
2

Sample Output:

6

Sample Input:

aaabbbb
2

Sample Output:

6

Sample Input:

abracadabra
10

Sample Output:

20

Note:

A tandem repeat of length 2n is string s, where for any position i (1 ≤ i ≤ n) the following condition fulfills: s_i = s_i + n.

In the first sample Kolya could obtain a string aabaab, in the second — aaabbbbbb, in the third — abracadabrabracadabra.