Dreamoon and Strings
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 
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 
as maximum value of 
over all s' that can be obtained by removing exactly x characters from s. Dreamoon wants to know 
for all x from 0 to |s| where |s| denotes the length of string s.
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.
Print |s| + 1 space-separated integers in a single line representing the 
for all x from 0 to |s|.
Input
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
Print |s| + 1 space-separated integers in a single line representing the for all x from 0 to |s|.
Samples
aaaaa
aa
2 2 1 1 0 0
axbaxxb
ab
0 1 1 2 1 1 0 0
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", ""}.