Consider the following program specification for evaluating a polynomial anx +an-1x-1 + ... + a1x + ao at x = C: Input: c, a0, a1, ..., an R Output: anch + an-1ch-1 + + a1c + ao +... Consider the following two implementations of this program specification: Implementation 1: Polynomial_1 Polynomial_1(c, ao, a1, ... , an) (1) 1 (2) yao (3) while in y+y+a; (4) Power(c, i) (5) i+i+1 (6) return y where Power is implemented as follows: Power(a, b) (1) i 0 (2) y 1 y-1 (3) while i < b (4) y y* a (5) i+i+1 (6) return y (6) return y Implementation 2 : Polynomial_2 Polynomial_2(c, ao, a₁, ... , an) (1) 1 (2) yan (3) while i ≤ n (4) y + y * c + an-i (5) ii+1 (6) return y Consider evaluating the polynomial 2x + x3 + 2x² + x + 3 at x = 2. Trace the execution of Polynomial_1 on this input by giving the value of y each time line (3) of Polynomial_1 is executed: The 1st time line (3) is executed, y = The 2nd time line (3) is executed, y = The 3rd time line (3) is executed, y = The 4th time line (3) is executed, y = The 5th time line (3) is executed, y = Trace the execution of Polynomial_2 on this input by giving the value of y each time line (3) of Polynomial_2 is executed: Trace the execution of Polynomial_2 on this input by giving the value of y each time line (3) of Polynomial_2 is executed: The 1st time line (3) is executed, y = The 2nd time line (3) is executed, y = The 3rd time line (3) is executed, y = The 4th time line (3) is executed, y = The 5th time line (3) is executed, y =