【競技プログラミング】Codeforces Round

[@ashishchokhani9084]

The distributive property of AND over XOR doesn't hold in general. However, since we are using 2^i here(in F), thats why we are able to perform XORs of all y's followed by multiplying with 2^i. If this is correct, can you help me to prove it or please correct me if I am wrong.

[@kotatsugame]

Where does the AND operation appear? I wasn't sure where you were referring to specifically. Are you sure you want to show XOR_y(y*2^i+k)=XOR_y(y)*2^i+XOR_y(k) in problem F?

[@ashishchokhani9084]

@@kotatsugame Sorry, Nvm. I was thinking * as AND operation. However, now it makes sense why the distribution holds because k

[@kotatsugame]

@@ashishchokhani9084 Yes, that's correct. Now multiplying by 2^i is the left shift operation, and adding k is the OR operation.