c++ vector with random unique elements with constant sum

I have an std::vector with fixed size N = 5. I want every element of the vector to be randomly selected between two positive numbers, in particular 1 and 12. (zeros are not allowed).Each element should be unique on the vector.

Code so far:

#include <algorithm>
#include <array>
#include <iostream>
#include <iterator>
#include <random>

int main() {
    std::random_device rd;
    std::mt19937 gen(rd());

    constexpr int MAX = 20;
    constexpr int LINES = 5;

    int sum{};
    int maxNum = 12;
    int minNum = 1;

    std::array<int, LINES> nums;

    for (int i = 0; i < LINES; ++i) {
        maxNum = std::min(maxNum, MAX - sum);
        minNum = std::min(maxNum, std::max(minNum, MAX - maxNum * (LINES - i)));
        std::cout << minNum << " " << maxNum << std::endl;
        std::uniform_int_distribution<> dist(minNum, maxNum);
        int num = dist(gen);

        nums[i] = num;
        sum += num;
    }

    std::shuffle(std::begin(nums), std::end(nums), gen);
    std::copy(std::begin(nums), std::end(nums), std::ostream_iterator<int>(std::cout, " "));
    std::cout << std::endl;
}