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.
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.
Print a single number — the maximum length of the tandem repeat that could have occurred in the new string.
A tandem repeat of length 2*n* is string *s*, where for any position *i* (1 ≤ *i* ≤ *n*) the following condition fulfills: *s*<sub class="lower-index">*i*</sub> = *s*<sub class="lower-index">*i* + *n*</sub>.

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