Problem9032--[yosupo] String - Z Algorithm

9032: [yosupo] String - Z Algorithm

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Time Limit : 1.000 sec  Memory Limit : 512 MiB

Description

Given a length $N$ string $S$. Calculate array $a_0, a_1, ..., a_{N - 1}$ as follows:
- $a_i$ is the LCP(longest common prefix) of $S$ and $S.substr(i)$.

Input

$S$

Output

$a_0$ $a_1$ $a_2$ ... $a_{N-1}$

Constraints

$1 \leq N \leq 5 \times 10^5$
Each character of $S$ is lowercase English letters.

Sample 1 Input

abcbcba

Sample 1 Output

7 0 0 0 0 0 1

Sample 2 Input

mississippi

Sample 2 Output

11 0 0 0 0 0 0 0 0 0 0

Sample 3 Input

ababacaca

Sample 3 Output

9 0 3 0 1 0 1 0 1

aaaaa

5 4 3 2 1

HINT

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