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.