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A. Substring and Subsequence
time limit per test
2 seconds
memory limit per test
256 megabytes
standard input
standard output

One day Polycarpus got hold of two non-empty strings s and t, consisting of lowercase Latin letters. Polycarpus is quite good with strings, so he immediately wondered, how many different pairs of " x y" are there, such that x is a substring of string s, y is a subsequence of string t, and the content of x and y is the same. Two pairs are considered different, if they contain different substrings of string s or different subsequences of string t. Read the whole statement to understand the definition of different substrings and subsequences.

The length of string s is the number of characters in it. If we denote the length of the string s as |s|, we can write the string as s = s 1 s 2... s |s|.

A substring of s is a non-empty string x = s[a... b] = s a s a + 1... s b (1 ≤ a ≤ b ≤ |s|). For example, "code" and "force" are substrings or "codeforces", while "coders" is not. Two substrings s[a... b] and s[c... d] are considered to be different if a ≠ c or b ≠ d. For example, if s="codeforces", s[2...2] and s[6...6] are different, though their content is the same.

A subsequence of s is a non-empty string y = s[p 1 p 2... p |y|] = s p 1 s p 2... s p |y| (1 ≤ p 1 < p 2 < ... < p |y| ≤ |s|). For example, "coders" is a subsequence of "codeforces". Two subsequences u = s[p 1 p 2... p |u|] and v = s[q 1 q 2... q |v|] are considered different if the sequences p and q are different.


The input consists of two lines. The first of them contains s (1 ≤ |s| ≤ 5000), and the second one contains t (1 ≤ |t| ≤ 5000). Both strings consist of lowercase Latin letters.


Print a single number — the number of different pairs " x y" such that x is a substring of string s, y is a subsequence of string t, and the content of x and y is the same. As the answer can be rather large, print it modulo 1000000007 (109 + 7).


Let's write down all pairs " x y" that form the answer in the first sample: " s[1...1] t[1]", " s[2...2] t[1]", " s[1...1] t[2]"," s[2...2] t[2]", " s[1...2] t[1 2]".