The quadratic expression that leaves remainders 1, 2 and 4 respectively when divided by (x - 1), (x - 2) and (x - 3) is

A

$$\frac{1}{2}(x^2 + x + 1)$$

B

$$\frac{1}{2}(x^2 - x + 1)$$

C

$$\frac{1}{2}(x^2 + x + 2)$$

D

$$\frac{1}{2}(x^2 - x + 2)$$