You are given three strings (s1,s2,s3). For each integer l (1 \le l \le 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.

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

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

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 \le i \le j \le |t|) represents the string titi+1... tj (substring of t from position i to position j inclusive).