Rune (rune)

Description

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Given a string \(s\) with a length of \(n\) and a string \(c\) with a length of \(m\), the defined level \(\operatorname{level(s,c)}\) represents the most in the string \(s\) How many strings \(c\) are there, pay attention to not overlapping each other.
Now you can delete any number of characters in any position.
You need to figure out the \(\text{level(s,c)}\) of the string \(s_i\) obtained after deleting \(i (0 \le i \le n)\) characters.

Format

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Input

The first line is the string \(s\).
The second line is the string \(c\).

Output

Output the number of \((n+1)\), the number of \(i\) represents the \(\text{level(s,c)}\) of the string \(s_{i-1}\) obtained after deleting \(i-1\) characters.

Sample

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Input

axbaxxb
ab

Output

0 1 1 2 1 1 0 0

Hint

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Data for \(20\%\): \(n \le 20, m \le 5\);
Data for \(60\%\): \(n \le 200, m \le 200\);
Data for \(100\%\): \(n \le 2000, m \le 500\).

Sample Code

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Code is not available!