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.

class Solution {
public:
    int numDistinct(string S, string T) {
        int m = T.length();
        int n = S.length();
        if (m > n) return 0;    
        vector<vector<int>> path(m+1, vector<int>(n+1, 0));
        for (int k = 0; k <= n; k++) path[0][k] = 1;    
    
        for (int j = 1; j <= n; j++) {
            for (int i = 1; i <= m; i++) {
                path[i][j] = path[i][j-1] + (T[i-1] == S[j-1] ? path[i-1][j-1] : 0);
            }
        }
    
        return path[m][n];
    }
};