Index Compression (Hard Version)

**This is the hard version of the problem. The difference is on the constraints of $N$, $T$ and sum of $N$. This problem is only scoreable in Div1 for 25 points** Given a parameter $M$, the score of an array $A = [A_1, A_2, ..., A_N]$ can be computed as follows : - Construct a new array $B = [B_1, B_2, ...., B_N]$ where $B_i$ is found as follows : - Let $S_i$ be a set containing all $A_j (