Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

A. Substring and Subsequence

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputOne 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*_{p1}*s*_{p2}... *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.

Input

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.

Output

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 (10^{9} + 7).

Examples

Input

aa

aa

Output

5

Input

codeforces

forceofcode

Output

60

Note

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]".

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jun/25/2019 15:55:40 (f3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|