Leetcode (Python): Distinct Subsequences

Given a string S and a string T, count the number of distinct subsequences of T in S.

A subsequence of a string is a new string which is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (ie, "ACE" is a subsequence of "ABCDE" while "AEC" is not).

Here is an example:
S = "rabbbit", T = "rabbit"

Return 3.

Solution:

class Solution:
    # @return an integer
    def numDistinct(self, S, T):
        numberOfSubsequences = [1]
        positions ={}
        for i in range (len(T)-1,-1,-1):
            numberOfSubsequences.append(0)
            if not T[i] in positions:
                positions[T[i]]=[]
            positions[T[i]].append(i)
        for i in range(0,len(S)):
            if S[i] in positions:
                for j in positions[S[i]]:
                    numberOfSubsequences[j+1]+=numberOfSubsequences[j]
        return numberOfSubsequences[len(T)]