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

Each command is one of the following two types: 

  1. Go 1 unit towards the positive direction, denoted as '+'
  2. Go 1 unit towards the negative direction, denoted as '-'



But the Wi-Fi condition is so poor that Dreamoon's smartphone reports some of the commands can't be recognized and Dreamoon knows that some of them might even be wrong though successfully recognized. Dreamoon 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 Drazil and list received by Dreamoon. What is the probability that Dreamoon ends in the position originally supposed to be final by Drazil's commands?

Input

The first line contains a string s1 — the commands Drazil sends to Dreamoon, this string consists of only the characters in the set {'+', '-'}. 

The second line contains a string s2 — the commands Dreamoon'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

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.

Examples

Input

++-+-
+-+-+


Output

1.000000000000


Input

+-+-
+-??


Output

0.500000000000


Input

+++
??-


Output

0.000000000000

Note

For the first sample, both s1 and s2 will lead Dreamoon to finish at the same position  + 1. 

For the second sample, s1 will lead Dreamoon 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.

Solution (in PYTHON3):

Solution:
from sys import stdin, stdout
from sys import maxsize
input = stdin.readline
#def print(n):
#    stdout.write(str(n)+'\n')


def solve():
    pass

def chose(n,r):
    r=max(r,n-r)
    ans=1
    for i in range(r+1,n+1):
        ans*=i
    for j in range(1,n-r+1):
        ans//=j
    return ans

test = 1
# test = int(input().strip())
for t in range(0, test):
    # n = int(input().strip())
    s1 = list(input().strip())                                                        # String Input, converted to mutable list.
    s2 = list(input().strip())
    c,c_,ex=0,0,0
    for el in s1:
        if(el=='+'):
            c+=1
        else:
            c-=1
    for el in s2:
        if(el=='+'):
            c_+=1
        elif(el=='-'):
            c_-=1
        else:
            ex+=1
    ans=0
    temp=ex-abs(c_-c)
    if(temp>=0 and temp%2==0):
        x=temp//2
        ans=chose(ex,x)
        ans=ans/(1<<ex)
    print(ans)
    # n, k = list(map(int, input().strip().split()))
    # arr = [int(x) for x in input().strip().split()]
    # brr = [list(map(int,input().strip().split())) for i in range(rows)]              # 2D array row-wise input
    ans = solve()


'''
rows, cols = (5, 5)
arr = [[0]*cols for j in range(rows)]                                         # 2D array initialization
rev_str=s[::-1]                                                               # To reverse given string
b=input().strip().split()                                                     # list created by spliting about spaces
brr = [[int(b[cols*i+j]) for j in range(cols)] for i in range(rows)]          # 2D array Linear Input
rows,cols=len(brr),len(brr[0])                                                # no of rows/cols for 2D array
arr.sort(key = lambda x : x[1])                                               # sort list of tuples by 2nd element, Default priority - 1st Element then 2nd Element
s=set()                                                                       # empty set
a=maxsize                                                                     # initializing infinity
b=-maxsize                                                                    # initializing -infinity
mapped=list(map(function,input))                                              # to apply function to list element-wise
try:                                                                          # Error handling
    #code 1
except:                                                                       # ex. to stop at EOF
    #code 2 , if error occurs
'''