CF443B.Kolya and Tandem Repeat

Kolya got string s for his birthday, the string consists of small English letters. He immediately added k more characters to the right of the string.

Then Borya came and said that the new string contained a tandem repeat of length l as a substring. How large could l be?

See notes for definition of a tandem repeat.

科里亚生日时收到了一个字符串 $s$，该字符串由小写英文字母组成。他立即在该字符串右侧添加了 $k$ 个额外字符。

随后鲍里亚指出，新字符串中包含一个长度为 $l$ 的并联重复子串（tandem repeat）。$l$ 的最大可能值是多少？

有关“并联重复”的定义，请参见注释部分。

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.

第一行包含字符串 $s$（$1 \le |s| \le 200$）。该字符串仅由小写英文字母组成。第二行包含整数 $k$（$1 \le k \le 200$）——待添加的字符个数。

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

输出一个整数——新字符串中可能出现的并联重复（tandem repeat）的最大长度。

A tandem repeat of length 2_n_ 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.

长度为 $2n$ 的并列重复串（tandem repeat）是指字符串 $s$，使得对任意位置 $i$（$1 \le i \le n$），均满足：$s_i = s_{i+n}$。

在第一个样例中，Kolya 可以得到字符串 aabaab；在第二个样例中，可得到 aaabbbbbb；在第三个样例中，可得到 abracadabrabracadabra。