Polynomial Class: Add and Multiply

/*
 * Problem : Process lines.
 * Input   : Two lines of coefficients.
 * Output  : Two result lines.
 * Approach: Operators or methods on the class.
 * Time    : O(n * m)
 * Space   : O(n + m)
 * Java    : 8 or newer.
 */
import java.util.Scanner;

public class Main {
        // Step 1: A Polynomial keeps its coefficients in an array. Index i is the coefficient of x^i.
        static class Polynomial {
            private final long[] coefficients;

            Polynomial(long[] coefficients) {
                // Step 2: Cut zero coefficients at the top, but keep one number.
                int size = coefficients.length;
                while (size > 1 && coefficients[size - 1] == 0) {
                    size--;
                }
                this.coefficients = java.util.Arrays.copyOf(coefficients, size);
            }

            // Step 3: Add the coefficients with the same power.
            Polynomial add(Polynomial other) {
                long[] result = new long[Math.max(coefficients.length, other.coefficients.length)];
                for (int i = 0; i < result.length; i++) {
                    long left = i < coefficients.length ? coefficients[i] : 0;
                    long right = i < other.coefficients.length ? other.coefficients[i] : 0;
                    result[i] = left + right;
                }
                return new Polynomial(result);
            }

            // Step 4: Multiply every term of one polynomial with every term of the other. Powers add up.
            Polynomial multiply(Polynomial other) {
                long[] result = new long[coefficients.length + other.coefficients.length - 1];
                for (int i = 0; i < coefficients.length; i++) {
                    for (int j = 0; j < other.coefficients.length; j++) {
                        result[i + j] += coefficients[i] * other.coefficients[j];
                    }
                }
                return new Polynomial(result);
            }

            @Override
            public String toString() {
                StringBuilder text = new StringBuilder();
                for (int i = 0; i < coefficients.length; i++) {
                    text.append(i == 0 ? "" : " ").append(coefficients[i]);
                }
                return text.toString();
            }

            static Polynomial parse(String line) {
                String[] part = line.trim().split("\\s+");
                long[] values = new long[part.length];
                for (int i = 0; i < part.length; i++) {
                    values[i] = Long.parseLong(part[i]);
                }
                return new Polynomial(values);
            }
        }

    // This method solves the task. It receives the input and returns the answer.
    static String[] solve(String[] lines) {
        Polynomial p = Polynomial.parse(lines[0]);
        Polynomial q = Polynomial.parse(lines[1]);
        return new String[] {"sum: " + p.add(q), "product: " + p.multiply(q)};
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        java.util.List<String> all = new java.util.ArrayList<>();
        while (scanner.hasNextLine()) {
            String line = scanner.nextLine().trim();
            if (!line.isEmpty()) {
                all.add(line);
            }
        }
        String[] lines = all.toArray(new String[0]);
        System.out.println(String.join("\n", solve(lines)));
    }
}