Consider the simple algorithm below (which should look very similar to part of Algorithm 5.1.1): Inputs: n,q [nonnegative integers], r[o,,rli 1 [an array of integers, each 0 or 1 Algorithm body: 1, r[i] := q mod 2 2, q:= q div 2 Outputs: n, q [nonnegative integers r[O], r[l], r[2], ..., rli [an array of integers, each 0 or 1] Suppose the inputs to this algorithm satisfy the relationship Prove that the output values of the algorithm will satisfy the relationship