Prefix Function Queries
Description
You are given a string $s$, consisting of lowercase Latin letters.
You are asked $q$ queries about it: given another string $t$, consisting of lowercase Latin letters, perform the following steps:
- concatenate $s$ and $t$;
- calculate the prefix function of the resulting string $s+t$;
- print the values of the prefix function on positions $|s|+1, |s|+2, \dots, |s|+|t|$ ($|s|$ and $|t|$ denote the lengths of strings $s$ and $t$, respectively);
- revert the string back to $s$.
The prefix function of a string $a$ is a sequence $p_1, p_2, \dots, p_{|a|}$, where $p_i$ is the maximum value of $k$ such that $k < i$ and $a[1..k]=a[i-k+1..i]$ ($a[l..r]$ denotes a contiguous substring of a string $a$ from a position $l$ to a position $r$, inclusive). In other words, it's the longest proper prefix of the string $a[1..i]$ that is equal to its suffix of the same length.
The first line contains a non-empty string $s$ ($1 \le |s| \le 10^6$), consisting of lowercase Latin letters.
The second line contains a single integer $q$ ($1 \le q \le 10^5$) — the number of queries.
Each of the next $q$ lines contains a query: a non-empty string $t$ ($1 \le |t| \le 10$), consisting of lowercase Latin letters.
For each query, print the values of the prefix function of a string $s+t$ on positions $|s|+1, |s|+2, \dots, |s|+|t|$.
Input
The first line contains a non-empty string $s$ ($1 \le |s| \le 10^6$), consisting of lowercase Latin letters.
The second line contains a single integer $q$ ($1 \le q \le 10^5$) — the number of queries.
Each of the next $q$ lines contains a query: a non-empty string $t$ ($1 \le |t| \le 10$), consisting of lowercase Latin letters.
Output
For each query, print the values of the prefix function of a string $s+t$ on positions $|s|+1, |s|+2, \dots, |s|+|t|$.
Samples
aba
6
caba
aba
bababa
aaaa
b
forces
0 1 2 3
1 2 3
2 3 4 5 6 7
1 1 1 1
2
0 0 0 0 0 0
aacba
4
aaca
cbbb
aab
ccaca
2 2 3 1
0 0 0 0
2 2 0
0 0 1 0 1