Palindromic characteristics

题面翻译

给你一个串，让你求出k阶回文子串有多少个。k从1到n。k阶子串的定义是：子串本身是回文串，而且它的左半部分也是回文串。 首先明确： 1、如果一个字串是k阶回文，那他一定还是k-1阶回文。 2、如果一个串是k阶回文，那么这个串需要满足： 1.它本是是回文的。 2.他的左半部分是k-1回文的。

题目描述

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.

输入格式

The first line contains the string $s$ ( $1<=|s|<=5000$ ) consisting of lowercase English letters.

输出格式

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

样例 #1

样例输入 #1

abba

样例输出 #1

6 1 0 0

样例 #2

样例输入 #2

abacaba

样例输出 #2

12 4 1 0 0 0 0

提示

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.