Distinct occurrences

Given two strings S and T of length n and m respectively. find count of distinct occurrences of T in S as a sub-sequence.

• Time : O(nm)
• Space : O(nm)

class Solution {
    int dp[8080][101];
    int mod = 1e9 + 7;
    int helper(string& s, string& t, int i, int j) {
        if(j == t.length()) return 1;
        if(i == s.length()) return 0;
        if(dp[i][j] != -1) return dp[i][j];
        int& res = dp[i][j] = helper(s, t, i + 1, j);
        if(s[i] == t[j]) res = (res + helper(s, t, i + 1, j + 1)) % mod;
        return res;
    }
public:
    int subsequenceCount(string S, string T) {
        memset(dp, -1, sizeof dp);
        return helper(S, T, 0, 0);
    }
};