Jacob has a piece of bread shaped like a figure 8, marked into sections and all initially connected as one piece of bread. The central part of the " 8 " is a single section, and each of the two loops of " 8 " is divided into an additional 1010 pieces. For each section, there is a 50 percent chance that Jacob will decide to cut it out and give it to a friend, and this is done independently for each section. The remaining sections of bread form some number of connected pieces. If E is the expected number of these pieces, and k is the smallest positive integer so that 2^{k}(E-\lfloor E\rfloor) \geq 1, find \lfloor E\rfloor+k. (Here, we say that if Jacob donates all pieces, there are 0 pieces left).