## Problem Implement an API in **C** to multiply two polynomials. A polynomial is represented by its coefficients. You must **define the input and output format** as if you were writing a small library function for other users. Example polynomials: - \(P(x) = x^3 - 2x + 5\) - \(Q(x) = x^2 + 2x + 4\) ## Requirements - Use **C (not C++)**. - Define a clear representation for a polynomial (e.g., array of coefficients where `coeff[i]` is the coefficient of \(x^i\)). - Provide a function (or set of functions) that multiplies two polynomials and returns the result. - Ensure the API handles: - Different degrees for the two inputs - Zero coefficients - Negative coefficients ## Output Return (or fill) a polynomial representing \(R(x) = P(x) \times Q(x)\) using your chosen representation. ## Constraints (you may assume) - Degrees are non-negative integers. - Coefficients fit in 32-bit signed integers (or specify a larger type if you choose). - Time complexity should be better than enumerating all exponent pairs explicitly as strings (i.e., use coefficient convolution).