Palindromic characteristics

题意翻译

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.

输入输出格式

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 $ .

输入输出样例

输入样例 #1

abba

输出样例 #1

6 1 0 0 

输入样例 #2

abacaba

输出样例 #2

12 4 1 0 0 0 0 

说明

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.