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.

The first line contains $ s $ ( $ 1

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

A tandem repeat of length $ 2n $ is string $ s $ , where for any position $ i $ ( $ 1