CF452E.Three strings

You are given three strings $(s_{1},s_{2},s_{3})$ . For each integer $l$ $(1<=l<=min(|s_{1}|,|s_{2}|,|s_{3}|)$ you need to find how many triples ( $i_{1},i_{2},i_{3}$ ) exist such that three strings $s_{k}[i_{k}...\ i_{k}+l-1]$ $(k=1,2,3)$ are pairwise equal. Print all found numbers modulo $1000000007 (10^{9}+7)$ .

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

First three lines contain three non-empty input strings. The sum of lengths of all strings is no more than $3·10^{5}$ . All strings consist only of lowercase English letters.

You need to output $min(|s_{1}|,|s_{2}|,|s_{3}|)$ numbers separated by spaces — answers for the problem modulo $1000000007 (10^{9}+7)$ .

Consider a string $t=t_{1}t_{2}...\ t_{|t|}$ , where $t_{i}$ 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 $t_{i}t_{i+1}...\ t_{j}$ (substring of $t$ from position $i$ to position $j$ inclusive).