#include <array>
#include <cstddef>
#include <vector>
#include <iostream>
 
template<typename T, int K, int N>
void generate_all_multisets(
    std::array<T, K> const& alphabet, 
    std::vector< std::vector<T> >& all_words, 
    std::vector<T>& current_word, 
    int current_letter
)
{
    if (current_letter == N) {
        all_words.push_back(current_word);
        for (auto k = 0; k != N; ++k) 
            std::cout << current_word[k];
        std::cout << "\n";
        return;
    }   
 
    auto const tmp = current_word[current_letter];
    for (auto letter = alphabet.begin(); letter != alphabet.end(); ++letter) {
        current_word[current_letter] = *letter;
        generate_all_multisets<T, K, N>(alphabet, all_words, current_word, current_letter + 1);
    }
    current_word[current_letter] = tmp; 
}
 
template<typename T, int K, int N>
void generate_all_words(
    std::array<T, K> const& alphabet, 
    std::vector< std::vector<T> >& all_words
)
{
    // first word
    std::vector<T> word(N, alphabet.front());
    generate_all_multisets<T, K, N>(alphabet, all_words, word, 0);
}
 
int main()
{
    std::array<int, 4> alphabet = { 1, 2, 3, 4};
    auto const word_length = 3; 
 
    std::vector< std::vector<int> > all_words;
    generate_all_words<int, 4, 3>(alphabet, all_words);
}

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