#include <iostream>
#include <vector>

using namespace std;

template<typename T>
class Polynomial {
private:
    vector<T> coef;

public:
    Polynomial(vector<T>& v){
        int index = v.size() - 1;
        while (v[index] == T()) {
            --index;
        }
        coef.resize(index + 1);
        for (int i = 0; i <= index; ++i) {
            coef[i] = v[i];
        }
    }

    Polynomial(T x = T()) {
        if (x != T()) {
            coef.resize(1, x);
        }
    }

    template<typename It>
    Polynomial(It begin, It end) {
        while (begin != end) {
            coef.push_back((*begin));
            ++begin;
        }
    }

    int Degree() const {
        return static_cast<int>(coef.size()) - 1;
    }

    T operator [](int i) const {
        if (i > (*this).Degree()) {
            return T();
        }
        return coef[i];
    }

    void normal() {
        int index = (*this).Degree();
        if (index == -1) {
            return;
        }
        while (coef[index] == T()) {
            --index;
        }
        vector<T> temp(index + 1);
        for (int i = 0; i <= index; ++i) {
            temp[i] = coef[i];
        }
        (*this) = Polynomial<T>(temp);
    }

    bool operator ==(const Polynomial<T>& other) const {
        Polynomial<T> temp1 = (*this);
        Polynomial<T> temp2 = other;
        temp1.normal();
        temp2.normal();
        if (temp1.Degree() != temp2.Degree()) {
            return false;
        }
        for (int i = 0; i < temp2.Degree(); ++i) {
            if (temp1[i] != temp2[i]) {
                return false;
            }
        }
        return true;
    }

    bool operator !=(const Polynomial<T>& other) const {
        return !((*this) == other);
    }

    typename vector<T>::const_iterator begin() const {
        return coef.begin();
    }

    typename vector<T>::const_iterator end() const {
        return coef.end();
    }

    Polynomial<T> operator +(const Polynomial<T>& other) const {
        vector<T> result(max((*this).Degree(), other.Degree()) + 1);
        for (int i = 0; i < min((*this).Degree(), other.Degree()) + 1; ++i) {
            result[i] = coef[i] + other[i];
        }
        if ((*this).Degree() > other.Degree()) {
            for (int i = other.Degree() + 1; i < (*this).Degree() + 1; ++i) {
                result[i] = coef[i];
            }
        } else {
            for (int i = (*this).Degree() + 1; i < other.Degree() + 1; ++i) {
                result[i] = other[i];
            }
        }
        auto ret = Polynomial(result);
        ret.normal();
        return ret;
    }

    Polynomial<T> operator -(const Polynomial<T>& other) const {
        vector<T> result(max((*this).Degree(), other.Degree()) + 1);
        for (int i = 0; i < min((*this).Degree(), other.Degree()) + 1; ++i) {
            result[i] = coef[i] - other[i];
        }
        if ((*this).Degree() > other.Degree()) {
            for (int i = other.Degree() + 1; i < (*this).Degree() + 1; ++i) {
                result[i] = coef[i];
            }
        } else {
            for (int i = (*this).Degree() + 1; i < other.Degree() + 1; ++i) {
                result[i] = T() - other[i];
            }
        }
        auto ret = Polynomial(result);
        ret.normal();
        return ret;
    }

    Polynomial<T>& operator +=(const Polynomial<T>& other) {
        (*this) = (*this) + other;
        return (*this);
    }

    Polynomial<T>& operator -=(const Polynomial<T>& other) {
        (*this) = (*this) - other;
        return (*this);
    }
};

template<typename T>
Polynomial<T> operator +(const T& self, const Polynomial<T>& other) {
    return Polynomial<T>(self) + other;
}

template<typename T>
Polynomial<T> operator -(const T& self, const Polynomial<T>& other) {
    return Polynomial<T>(self) - other;
}

template<typename T>
bool operator ==(const T& self, const Polynomial<T>& other) {
    return Polynomial<T>(self) == other;
}

template<typename T>
bool operator !=(const T& self, const Polynomial<T>& other) {
    return Polynomial<T>(self) != other;
}