Another simple (although not so efficient) way to generate these permutations in lexical order is to start with the permutations {1, 1, 1, ..., 1}. The next permutation in each case is generated by scanning the current permutation from right to left until we encounter an element that has not attained its maximum value. This element is incremented by one, and all elements to the right of it are reset to their lowest allowable values and so the process repeats. Implement this algorithm.