I think i chose the wrong word . Actually there is no problem . We cannot say an output is the original output because, according to the definition of egyptian fractions, An Egyptian fraction of a given fraction is the sum of distinct unit fractions. Thus the only condition is that the denominators should be unique. Thus 7/12 = 1/2 + 1/12 or 7/12 = 1/3 + 1/6 + 1/12.