494B · Obsessive String

Problem: 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, ..., ak and b1, b2, ..., bk satisfying the following requirements:

• k ≥ 1
• $$$$
• $\forall i \left( 1 \leq i \leq k \right) b_i \geq a_i$
• $\forall i \left( 2 \leq i \leq k \right) a_i > b_{i-1}$
• $\forall i \left( 1 \leq i \leq k \right)$  t is a substring of string saisai + 1... sbi (string s is considered as 1-indexed).

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

Input Format: Input consists of two lines containing strings s and t (1 ≤ |s|, |t| ≤ 105). Each string consists of lowercase Latin letters.

Output Format: Print the answer in a single line.