Hamed has recently found a string t and suddenly became quite fond of it. He spent several days trying to find all occurrences of t in other strings he had. Finally he became tired and started thinking about the following problem. Given a string s how many ways are there to extract k ≥ 1 non-overlapping substrings from it such that each of them contains string t as a substring? More formally, you need to calculate the number of ways to choose two sequences a₁, a₂, ..., a_k and b₁, b₂, ..., b_k satisfying the following requirements:

• k ≥ 1
• 
• 
• 
•   t is a substring of string s_ais_ai + 1... s_bi (string s is considered as 1-indexed).

As the number of ways can be rather large print it modulo 10⁹ + 7.