Sequence Operations

Transform a sequence using $X_i=2\sum_{k<i}A_k+A_i$. After removing position $i$, consider a later position $j$. If $j-i$ is odd, the preceding sum decreases by $A_i$ and that element increases by $2A_i$. If it is even, the preceding sum increases by $A_i$ and the element decreases by $2A_i$. Thus its transformed value is unchanged. The operation simply deletes one transformed value. The transformation is invertible: given the preceding sum $P$, recover the next element as $X_i-2P$. Therefore equal resulting sequences correspond exactly to common subsequences of the transformed sequences. If their LCS has length $L$, the answer is $N+M-2L$. For subtask 1, enumerate actual deletion states and compare common states. There are at most $2^N$ states; an ordered-set implementation has the conservative bound $O((2^N+2^M)(N+M)^3)$. The full solution uses LCS DP in $O(NM)$ time and $O(M)$ memory. Initially $|X_i|\le49\,995\,000$. Every later transformed sequence is a subsequence, so every reconstructed element has magnitude at most $(2\cdot5000-1)49\,995\,000<5\cdot10^{11}$. Signed 64-bit integers suffice. Solution written by GPT6.1