Fine and Wilf words for any periods II

Given positive integers n, and p1,…,pr, we establish a fast word combinatorial algorithm for constructing a word w=w1⋯wn of length n, with periods p1,…,pr, and on the maximal number of distinct letters. Moreover, we show that the constructed word, which is unique up to word isomorphism, is a pseudo-palindrome — i.e. it is a fixed point of an involutory antimorphism.