I can't understand the problem in my solution described below

We can create a tree and then find the pattern as follows:

As can be seen above, there are only 8 possible numbers (not necessarily distinct) shown below: {0, x, x&k, x|k, ()&k, x&(), x^k, k}

So we can create a transition table for each of these numbers for each of the possiblities of AND, OR, XOR. Using this logic I arrived at this solution

But the program is giving incorrect answer. Can someone point out the flaw in logic and/or implementation, please.