Description

You are given definitions of multiple polynomials, such as F(x)=+2x^2 +3x +1 and G(x)=+2x +1 , along with several operations to perform on these polynomials, like F(2)+G(3), You need to compute the results of these operations.

This problem is a partial judge.
Please implement functions defined in the header file:

• Polynomial(int deg, const int *coeffs) Constructor: Initializes polynomial with degree and coefficient array 
• Polynomial(const Polynomial& other) Copy constructor: Creates a copy of another polynomial 
• Polynomial operator+(const Polynomial& other) const Addition operator: Adds two polynomials 
• Polynomial operator-(const Polynomial& other) const Subtraction operator: Subtracts one polynomial from another 
• Polynomial operator*(const Polynomial& other) const Multiplication operator: Multiplies two polynomials
• Polynomial& operator=(const Polynomial& other) Assignment operator: Assigns one polynomial to another
• int evaluate(int x) const Evaluates polynomial at given value x, The result must be taken modulo 10⁹+7.  If the result is negative, add 10⁹+7 after taking the modulo to ensure the final answer is non-negative.
• friend std::ostream& operator<<(std::ostream& os, const Polynomial& poly) Output stream operator: Prints polynomial to output stream

Input

The first line contains two positive integers n and m, where n is the number of polynomials, and m is the number of operations to perform

The next n lines describe the polynomials. Each line is in one of two formats:

1. <symbol> = <polynomial>, which defines the mathematical expression for that polynomial (e.g., "F = 2x^2 + 3x + 1").
2. <symbol1> = <symbol2>, which means the polynomial defined by <symbol1> is the same as the polynomial defined by <symbol2>.

• <func1> and <func2> are the names of two polynomials.
• <op> is an operator, which can be +, -, or *, indicating the operation to perform (addition, subtraction, or multiplication).
• <x> is the value of x to substitute into the polynomials

Constraints

• The degree of each polynomial is at most 100.
• 1 <= n <= 26
• 1 <= m <= 1000
• All coefficients and values in the polynomials are less than or equal to 10⁵
• The symbol will only consist of a single uppercase letter.

Subtasks

• testcase 1: The operation will only involve addition (+)
• testcase 2: The operation will only involve subtraction (-)
• testcase 3: The operation will only involve multiplication (*)
• testcases 4 ~ 6: No additional restrictions

Output

• <poly> is the mathematical expression of the resulting polynomial after performing the operation on <func1> and <func2>.
• <ans> is the value of the resulting polynomial evaluated at x = x.
• The result <ans> must be taken modulo 10⁹+7.  If the result is negative, add 10⁹+7 after taking the modulo to ensure the final answer is non-negative.

Sample Input  Download

Sample Output  Download

Partial Judge Code

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