-snip-
PS. Actually instead of solving pk110 within the range [2^109 ... 2^110-1] the program solves the key pk110s within the range [0 ... 2^109-1]
Thanks for the detailed answer. This is very clear now.
Can you help make it clear to me

So the tames work from range 0...meaning 0x0 to 0x3FFFFFFFFFFFFFFFFFFFFFFFFFFFF (for pubkey 110)?