Write C# program with proof of correctness (loop invariant) using a single "while" loop and no arrays:

The program inputs an integer n greater than 1 and receives a sequence of real numbers x c_1 c_2 c_3 ... c_n from the console. It outputs the value of a polynomial x^n+c_1*x^{n-1}+c2*x^{n-2}+c_3 * x^{n-3}+...c_{n-1}*x+c_n.