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: dp.

class Solution {
public:
    int numDistinct(string S, string T) {
        int N = S.size(), M = T.size();
        int dp[M+1][N+1];
        dp[0][0] = 1;
        for (int j = 1; j <= N; ++j)
            dp[0][j] = 1;
        for (int i = 1; i <= M; ++i)
            dp[i][0] = 0;

        for (int i = 1; i <= M; ++i)
            for (int j = 1; j <= N; ++j)
                if (S[j-1] == T[i-1])
                    dp[i][j] = dp[i][j-1] + dp[i-1][j-1];
                else
                    dp[i][j] = dp[i][j-1];

        return dp[M][N];
    }
};