CF835D Palindromic characteristics

Palindromic characteristics of string $ s $ with length $ |s| $ is a sequence of $ |s| $ integers, where $ k $ -th number is the total number of non-empty substrings of $ s $ which are $ k $ -palindromes. A string is $ 1 $ -palindrome if and only if it reads the same backward as forward. A string is $ k $ -palindrome ( $ k>1 $ ) if and only if: 1. Its left half equals to its right half. 2. Its left and right halfs are non-empty ( $ k-1 $ )-palindromes. The left half of string $ t $ is its prefix of length $ ⌊|t|/2⌋ $ , and right half — the suffix of the same length. $ ⌊|t|/2⌋ $ denotes the length of string $ t $ divided by $ 2 $ , rounded down. Note that each substring is counted as many times as it appears in the string. For example, in the string "aaa" the substring "a" appears 3 times.

The first line contains the string $ s $ ( $ 1

Print $ |s| $ integers — palindromic characteristics of string $ s $ .

In the first example 1-palindromes are substring «a», «b», «b», «a», «bb», «abba», the substring «bb» is 2-palindrome. There are no 3- and 4-palindromes here.