Grid Unique Paths

# from math import factorial as f
class Solution:
    # @param A : integer
    # @param B : integer
    # @return an integer

    hmap = {0:1, 1:1}
    def factorial(self, n):
        if n not in self.hmap:
            ans = n * self.factorial(n-1)
            self.hmap[n] = ans
        return self.hmap[n]

    # def countPaths(self, X, Y, x, y):
    #     if x == X-1 and y == Y-1:
    #         return 1
    #     elif x == X-1:
    #         return self.countPaths(X, Y, x, y+1)
    #     elif y == Y-1:
    #         return self.countPaths(X, Y, x+1, y)
    #     else:
    #         return self.countPaths(X, Y, x+1, y) + self.countPaths(X, Y, x, y+1)

    # def countPaths(self, x, y):
    #     if x == 1 or y == 1:
    #         return 1
    #     else:
    #         return self.countPaths(x-1, y) + self.countPaths(x, y-1)


    def uniquePaths(self, A, B):
       # return self.countPaths(A, B, 0, 0)
       #hmap = {0:1, 1:1}
       ##return self.countPaths(A, B)
       #x = min(A, B)-1
       #y = max(B, A)-1
       #xf = self.factorial(x)
       #yf = self.factorial(y)
       #return self.factorial(x+y)//(xf*yf)

        total = A + B - 2
        smaller = min(A - 1, B - 1)
        nom = 1
        den = 1
        for i in range(smaller):
            nom *= total - i
            den *= i + 1
        return nom//den

       # return self.factorial(A+B-2)/((self.factorial(A-1))*(self.factorial(B-1)))

       #grid = [[1 for x in range(B)] for x in range(A)]
       #for r in range(1, A):
       #    for c in range(1, B):
       #        grid[r][c] = grid[r-1][c] + grid[r][c-1]
       #return grid[A-1][B-1]