Xor Table

There are two integer sequences $A_1, A_2, \dots, A_N$ and $B_1, B_2, \dots, B_M$. You do not know the exact values of their elements, but you know that $L_i \le A_i \le R_i$ for each valid $i$ and $P_i \le B_i \le Q_i$ for each valid $i$. You also have a matrix $C$ with $N$ rows and $M$ columns. Some elements of $C$ are missing. For each element $C_{i, j}$ ($1 \le i \le N$, $1 \le j \le M$) that