Description:
Dreamoon has a string s and a pattern string p. He first removes exactly x characters from s obtaining string s' as a result. Then he calculates $$\mathsf{occ}(s',p)$$ that is defined as the maximal number of non-overlapping substrings equal to p that can be found in s'. He wants to make this number as big as possible.
More formally, let's define $$\operatorname{ans}(x)$$ as maximum value of $$\mathsf{occ}(s',p)$$ over all s' that can be obtained by removing exactly x characters from s. Dreamoon wants to know $$\operatorname{ans}(x)$$ for all x from 0 to |s| where |s| denotes the length of string s.
Input Format:
The first line of the input contains the string s (1 ≤ |s| ≤ 2 000).
The second line of the input contains the string p (1 ≤ |p| ≤ 500).
Both strings will only consist of lower case English letters.
Output Format:
Print |s| + 1 space-separated integers in a single line representing the $$\operatorname{ans}(x)$$ for all x from 0 to |s|.
Note:
For the first sample, the corresponding optimal values of s' after removal 0 through |s| = 5 characters from s are {"aaaaa", "aaaa", "aaa", "aa", "a", ""}.
For the second sample, possible corresponding optimal values of s' are {"axbaxxb", "abaxxb", "axbab", "abab", "aba", "ab", "a", ""}.