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 l1 = s.length();
        int l2 = t.length();
        
        int dp[l1+1][l2+1];
        for(int i=0;i<l1+1;i++){
            for(int j=0;j<l2+1;j++){
                if(i==0 && j==0){
                    dp[i][j] = 1;
                }else if (i==0){
                    dp[i][j] = 0;
                }else if(j==0){
                    dp[i][j] = 1;
                }else {
                    if(s[i-1] == t[j-1]){
                        dp[i][j] = dp[i-1][j-1] + dp[i-1][j];
                    }else {
                        dp[i][j] = dp[i-1][j];
                    }
                }
            }
        }
        return dp[l1][l2];
    }
};