Obsessive String

2000ms

262144K

Description:

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
$\text{[math]}$
$\text{[math]}$
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$\text{[math]}$ t is a substring of string s_{a_i}s_{a_i + 1}... s_{b_i} (string s is considered as 1-indexed).