import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import java.util.stream.Collectors;

public class PolynomialTask {
    private int n;

    private List<Integer> firstPolynomial;
    private List<Integer> secondPolynomial;

    public PolynomialTask(int n, List<Integer> firstPoly, List<Integer> secondPoly) {
        this.n = n;
        this.firstPolynomial = firstPoly;
        this.secondPolynomial = secondPoly;
    }

    public Integer[] multiplyPolynomials(List<Integer> firstPolynomial, List<Integer> secondPolynomial) {
        int[] multiplied = new int[firstPolynomial.size() + secondPolynomial.size() - 1];
        int sizeOfFirstPoly = firstPolynomial.size();
        int sizeOfSecondPoly = secondPolynomial.size();
        for (int i = 0; i < sizeOfFirstPoly; i++) {
            for (int j = 0; j < sizeOfSecondPoly; j++)
                multiplied[i + j] = (multiplied[i + j] + (firstPolynomial.get(i) * secondPolynomial.get(j))) % n;
        }
        return Arrays.stream(multiplied).boxed().toArray(Integer[]::new);
    }

    public int[] moduloDividePolynomialsReturnQuotient(List<Integer> firstPoly, List<Integer> secondPoly) throws MultiplierNotFoundException, DivisionErrorException {
        int[] quotient = new int[firstPoly.size() + secondPoly.size()];
        int firstPolyDegree = firstPoly.size() - 1;
        int secondPolyDegree = secondPoly.size() - 1;
        List<Integer> polynomialAfterSubtract = firstPoly;


        while (firstPolyDegree >= secondPolyDegree) {
            polynomialAfterSubtract = calcQuotient(polynomialAfterSubtract, secondPoly, quotient);
            firstPolyDegree = polynomialAfterSubtract.size() - 1;
        }

        int[] remainder = new int[polynomialAfterSubtract.size()];
        for (int i = 0; i < polynomialAfterSubtract.size(); i++) {
            remainder[i] = polynomialAfterSubtract.get(i);
        }
        return remainder;
    }

    private List<Integer> calcQuotient(List<Integer> firstPoly, List<Integer> secondPoly, int[] quotient) throws MultiplierNotFoundException, DivisionErrorException {
        int firstPolyDegree = firstPoly.size() - 1;
        int secondPolyDegree = secondPoly.size() - 1;
        if (firstPolyDegree < secondPolyDegree) {
            throw new DivisionErrorException();
        }
        int quotientCoefficient;
        if ((((float) firstPoly.get(firstPolyDegree) / (float) secondPoly.get(secondPolyDegree))) == Math.round(firstPoly.get(firstPolyDegree) / secondPoly.get(secondPolyDegree))) {
            quotientCoefficient = firstPoly.get(firstPolyDegree) / secondPoly.get(secondPolyDegree);
        } else {
            quotientCoefficient = invElem(firstPoly.get(firstPolyDegree), secondPoly.get(secondPolyDegree));
        }
        quotient[firstPolyDegree - secondPolyDegree] += quotientCoefficient;
        List<Integer> newPoly = generatePolyFromIndexAndValue(firstPolyDegree - secondPolyDegree, quotientCoefficient);
        Integer[] multipliedPolynomials = multiplyPolynomials(newPoly, secondPoly);
        List<Integer> polynomialAfterFirstDivide = new ArrayList<>(Arrays.asList(multipliedPolynomials));

        return removeUnnecessaryZeros(subtractTwoPolynomials(firstPoly, polynomialAfterFirstDivide));
    }

    private List<Integer> removeUnnecessaryZeros(List<Integer> polynomialAfterSubtract) {
        int amountOfZeros = 0;
        for (int i = polynomialAfterSubtract.size() - 1; i >= 0; i--) {
            if (polynomialAfterSubtract.get(i) == 0) {
                amountOfZeros++;
            } else {
                break;
            }
        }

        polynomialAfterSubtract = polynomialAfterSubtract.subList(0, polynomialAfterSubtract.size() - amountOfZeros);
        return polynomialAfterSubtract;
    }

    private List<Integer> subtractTwoPolynomials(List<Integer> firstPoly, List<Integer> secondPoly) {
        List<Integer> subtractedPolynomial = new ArrayList<>(Collections.nCopies(firstPoly.size() + secondPoly.size(), 0));
        for (int index = firstPoly.size(); index >= 0; index--) {
            if (index < secondPoly.size()) {
                subtractedPolynomial.set(index, firstPoly.get(index) - secondPoly.get(index));
                parseNegativeElement(subtractedPolynomial, index);
            }
        }
        return subtractedPolynomial;
    }

    private void parseNegativeElement(List<Integer> subtractedPolynomial, int index) {
        while (subtractedPolynomial.get(index) < 0)
            subtractedPolynomial.set(index, (subtractedPolynomial.get(index) * subtractedPolynomial.get(index)) % n);
    }

    private List<Integer> generatePolyFromIndexAndValue(int size, int quotientCoefficient) {
        List<Integer> poly = new ArrayList<>(Collections.nCopies(size + 1, 0));
        poly.set(size, quotientCoefficient);
        return poly;
    }

    private int invElem(int a, int b) throws MultiplierNotFoundException {

        for (int i = 0; i < n; i++) {
            if (a == (b * i) % n) {
                return i;
            }
        }

        throw new MultiplierNotFoundException();
    }

    public void printAllValuesToStandardOutput() throws DivisionErrorException, MultiplierNotFoundException {
        List<List<Integer>> values = new ArrayList<>();
        values.add(Arrays.asList(multiplyPolynomials(firstPolynomial, secondPolynomial)));
        values.add(Arrays.stream(moduloDividePolynomialsReturnQuotient(firstPolynomial, secondPolynomial)).boxed().collect(Collectors.toList()));
        try {
            values.add(gcd(firstPolynomial, secondPolynomial));
        } catch (MultiplierNotFoundException e) {
        }
        System.out.println(values);
    }

    private List<Integer> gcd(List<Integer> polyOne, List<Integer> polyTwo) throws MultiplierNotFoundException, DivisionErrorException {
        if (polyTwo.isEmpty()) return polyOne;
        List<Integer> poly = Arrays.stream(moduloDividePolynomialsReturnQuotient(polyOne, polyTwo)).boxed().collect(Collectors.toList());
        return gcd(polyTwo, poly);

    }

}