Problem2956--Three strings

2956: Three strings

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

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Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given three strings (s1,s2,s3). For each integer l (1≤l≤min(|s1|,|s2|,|s3|) you need to find how many triples (i1,i2,i3) exist such that three strings sk[ik... ik+l-1] (k=1,2,3) are pairwise equal. Print all found numbers modulo 1000000007(109+7).

See notes if you are not sure about some of the denotions used in the statement.

Input

First three lines contain three non-empty input strings. The sum of lengths of all strings is no more than 3·105. All strings consist only of lowercase English letters.

Output

You need to output min(|s1|,|s2|,|s3|) numbers separated by spaces − answers for the problem modulo 1000000007(109+7).

Examples
Input
abc
bc
cbc
Output
3 1
Input
abacaba
abac
abcd
Output
11 2 0 0
Note

Consider a string t=t1t2... t|t|, where ti denotes the i-th character of the string, and |t| denotes the length of the string.

Then t[i... j] (1≤i≤j≤|t|) represents the string titi+1... tj (substring of t from position i to position j inclusive).

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