Receive The Signal
Difficulty: Hard

Lagnajeet is standing at the position 0 on a number line. Sunil is sending a list of commands through Wi-Fi to Lagnajeet's smartphone and Lagnajeet follows them.

Each command is one of the following two types:

Go 1 unit towards the positive direction, denoted as '+'
Go 1 unit towards the negative direction, denoted as '-'
But the Wi-Fi condition is so poor that Lagnajeet's smartphone reports some of the commands can't be recognized and Lagnajeet knows that some of them might even be wrong though successfully recognized. Lagnajeet decides to follow every recognized command and toss a fair coin to decide those unrecognized ones (that means, he moves to the 1 unit to the negative or positive direction with the same probability 0.5).

You are given an original list of commands sent by Sunil and list received by Lagnajeet. What is the probability that Lagnajeet ends in the position originally supposed to be final by Sunil's commands?

__Input__<br>
The first line contains a string s1 — the commands Sunil sends to Lagnajeet, this string consists of only the characters in the set {'+', '-'}.

The second line contains a string s2 — the commands Lagnajeet's smartphone recognizes, this string consists of only the characters in the set {'+', '-', '?'}. '?' denotes an unrecognized command.

Lengths of two strings are equal and do not exceed 10.

__Output__<br>
Output a single real number corresponding to the probability. The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 9.

__Sample test(s)__<br>

__input__<br>
++-+-<br>
+-+-+

__output__<br>
1.000000000000

__input__<br>
+-+-<br>
+-??

__output__<br>
0.500000000000

__input__<br>
+++<br>
??-

__output__<br>
0.000000000000

__Note__<br>
For the first sample, both s1 and s2 will lead Lagnajeet to finish at the same position  + 1.

For the second sample, s1 will lead Lagnajeet to finish at position 0, while there are four possibilites for s2: {"+-++", "+-+-", "+--+", "+---"} with ending position {+2, 0, 0, -2} respectively. So there are 2 correct cases out of 4, so the probability of finishing at the correct position is 0.5.

For the third sample, s2 could only lead us to finish at positions {+1, -1, -3}, so the probability to finish at the correct position  + 3 is 0.

Input Format:

Output Format:

Sample Input:

Sample Output:

Python 3 starter code:


Reference solution (Unknown):
http://ideone.com/MgyHDW