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) 
    {
        if(T.length()==0) return 0;
        
           int n=S.length();
           int path[n];
           
           for(int i=0;i<n;i++) 
           if(S[i]==T[0]) path[i]=1;
           else path[i]=0;
           
           int sum;
           for(int i=1;i<T.length();i++)
           {
               sum=0;
               for(int k=0;k<n;k++)
               {
                   int sum2=0;
                   if(T[i]==S[k]) sum2=sum;
                   if(path[k]>0) sum=sum+path[k];
                   path[k]=sum2;
               }
           }
           
           sum=0;
           for(int i=0;i<n;i++)
            sum=sum+path[i];
        return sum;
    }
};