Distinct Subsequences DP explanation

From LeetCode

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.

I see a very good DP solution, however, I have hard time to understand it, anybody can explain how this dp works?

int numDistinct(string S, string T) {

    vector<int> f(T.size()+1);

    //set the last size to 1.
    f[T.size()]=1;

    for(int i=S.size()-1; i>=0; --i){
        for(int j=0; j<T.size(); ++j){
            f[j]+=(S[i]==T[j])*f[j+1];
            printf("%d\t", f[j] );
        }
        cout<<"\n";
    }
    return f[0];
}