Coderbyte Python Challenge: ChessboardTravelling

ChessboardTravelling.py

# Function input is a string that are the coordinates of a space on a 8x8
# chess board. The structure of str will be (x y)(a b) where (x y) is the
# current position and (a b) is the new position.

# a and b will be strictly greater than x and y respectively.

# Program will determine the number of ways there are of travelling from
# (x y) to (a b) by only travelling up and right.

def ChessboardTraveling(str):

    # import math to get factorial function
    import math

    # convert the string into integer to define x, y, a and b
    x = int(str[1])
    y = int(str[3])
    a = int(str[6])
    b = int(str[8])

    # make sure and b is greater than x and y
    if (a <= x) or (b <= y):
        print "Please provide us coorindates where a > x and b > y such that str = (x y)(a b)..."

    # create var solutions to track the number of solutions available
    solutions = 0

    # define differences, if differene is 2 then solutions is 2q
    # otherwise get nth solutions
    if a > x and b > y:
        diff = (a-x) + (b-y)
        diff_a = a - x
        diff_b = b - y
        if diff == 2:
            solutions = 2
        else:
            solutions = math.factorial(diff_a+diff_b) / (math.factorial(diff_a) * math.factorial(diff_b))
    
    return int(solutions)
    
print ChessboardTraveling(raw_input())