Comparing two polynomials with vector's coefficients C++

This code is supposed to output the largest coefficient of 2 different polynomials, but if the first one is larger than the second, it doesn't compile correctly.

So, if the first polynomial is 1 - 2x +4x^3 and the second polynomial is -x + 5x^2 - 3x^6. It will work since the second polynomial is larger than the first.

It posts a "vector subscript out of range" error whenever the first polynomial is larger than the second

class Polynomial {
public:
Polynomial();
Polynomial(const vector<int>& coeffs);

int Degree() const;
int Coefficient(int k) const;
void print() const;
private:
vector<int>coefficient;

int main(){
//Variable and vector for inputs
vector<int> coefficient;
int input = 0;
//Welcome message
cout << "Welcome! Please input the coefficients of the first polynomial p(x).\nWhen you are finished, enter -12345.\n";

//While loop - if input isn't -12345, put the input into coefficient.
while (input != -12345){
    cin >> input;
    coefficient.push_back(input);
}

//Deletes -12345
coefficient.pop_back();

//Puts coefficient values into constructor
Polynomial first(coefficient);

//Prints first polynomial
cout << "\nYour first polynomial is p(x) = ";
first.print();

//Prints degrees of first polynomial
cout << ".\np(x) has degree " << first.Degree();
int degree1 = first.Degree();

//Prints transformation of first polynomial
cout << ".\nThe transform of p(x) is ";
first.Transform();

//clears the values in coefficient for second polynomial inputs.
coefficient.clear();

//Inputs the second polynomial's coefficients.
cout << ".\n\nPlease input the coefficients of the second polynomial q(x).\n";
//Had to use do-while because while loop wouldn't work.
do {
    cin >> input;
    coefficient.push_back(input);

} while (input != -12345);

//Deletes -12345
coefficient.pop_back();

//Puts coefficients into second polynomial
Polynomial second(coefficient);

//Prints second polynomial
cout << "\nYour second polynomial is q(x) = ";
second.print();

cout << ".\nq(x) has degree " << second.Degree();
int degree2 = second.Degree();

if (degree1 > degree2){
    cout << ".\n\nThe coefficient of x^" << degree1 << " in p(x) is " << first.Coefficient(degree1);
    cout << ".\nThe coefficient of x^" << degree1 << " in q(x) is " << second.Coefficient(degree1);
}
else{
    cout << ".\n\nThe coefficient of x^" << degree2 << " in p(x) is " << first.Coefficient(degree2);
    cout << ".\nThe coefficient of x^" << degree2 << " in q(x) is " << second.Coefficient(degree2);
}

int Polynomial::Degree() const{
int number = 0;
for (size_t i = 0, size = coefficient.size(); i < size; i++){
    if (coefficient[i] != 0)
        number = i;
}
return number;
}

int Polynomial::Coefficient(int k) const{
if (coefficient[k] != 0)
    return coefficient[k];
else
    return 0;
}