E. Prefix Function Queries
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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:

1. concatenate $s$ and $t$;
2. calculate the prefix function of the resulting string $s+t$;
3. 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);
4. 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.

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 $|s|+1, |s|+2, \dots, |s|+|t|$.

Examples
Input
aba
6
caba
aba
bababa
aaaa
b
forces
Output
0 1 2 3
1 2 3
2 3 4 5 6 7
1 1 1 1
2
0 0 0 0 0 0
Input
aacba
4
aaca
cbbb
aab
ccaca
Output
2 2 3 1
0 0 0 0
2 2 0
0 0 1 0 1