Let a, b, c, d be four integers such that a+b+c+d = 4m+1 where m is a positive integer. Given m, which one of the following is necessarily true?

A

The minimum possible value of $$a^2 + b^2 + c^2 + d^2$$ is $$4m^2-2m+1$$

B

The minimum possible value of $$a^2 + b^2 + c^2 + d^2$$ is $$4m^2+2m+1$$

C

The maximum possible value of $$a^2 + b^2 + c^2 + d^2$$ is $$4m^2-2m+1$$

D

The maximum possible value of $$a^2 + b^2 + c^2 + d^2$$ is $$4m^2+2m+1$$