Interleaving String

Given s1, s2, s3, find whether s3 is formed by the interleaving of s1 and s2.
For example,
Given:
s1 = "aabcc",
s2 = "dbbca",
When s3 = "aadbbcbcac", return true.
When s3 = "aadbbbaccc", return false.

Solution: 1. dp. O(MN) time & space. 'dp[i][j] == true' means that there is at least one way to construct
the string s3[0...i+j-1] by interleaving s1[0...j-1] and s2[0...i-1].
2. Recursion. Okay for Small but TLE for Large Test data.

class Solution {
public:
    bool isInterleave(string s1, string s2, string s3) {
        int M = s1.size(), N = s2.size(), K = s3.size();
        if (M + N != K) return false;
        
        int dp[N+1][M+1];
        for (int i = 1; i <= N; ++i)
            dp[i][0] = s2[i-1] == s3[i-1];
        for (int j = 1; j <= M; ++j)
            dp[0][j] = s1[j-1] == s3[j-1];

        for (int i = 1; i <= N; ++i)
            for (int j = 1; j <= M; ++j)
                dp[i][j] = dp[i-1][j] && s2[i-1] == s3[i+j-1] ||
                           dp[i][j-1] && s1[j-1] == s3[i+j-1];

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