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 s_k[i_k... i_k + 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).

Note

Consider a string t = t₁t₂... 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_it_i + 1... t_j (substring of t from position i to position j inclusive).

Three strings

Examples