Luffy is playing with some magic boxes and a machine. Each box has a value(number) inside. Opening a box, Luffy sees the value, adds the value to his score(if the box value is negative, Luffy loses points) and destroys the box. Putting a box of value $X$ in the machine, this box vanishes and it is replaced by two new boxes of values $X+1$ and $X-1$(it's not known which one has the respective value, but he can identify the new boxes). At the beginning, Luffy has $0$ points and has a box whose value is known(it is zero). a) Prove that Luffy can reach at least $1000$ points b) Is it possible that Luffy reaches at least $1000000$ points, without have less than $-42$ points in any moment?