5403: Obsessive String

内存限制:256 MB 时间限制:2 S
题面:传统 评测方式:文本比较 上传者:
提交:8 通过:7

题目描述


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
  • 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
Input consists of two lines containing strings s and t (1≤|s|,|t|≤105). Each string consists of lowercase Latin letters.
Output
Print the answer in a single line.
Examples
Input
ababa
aba
Output
5
Input
welcometoroundtwohundredandeightytwo
d
Output
274201
Input
ddd
d
Output
12

输入样例 复制


输出样例 复制