Let f(x) = x^{3} + px^{2} + qx + r, where p,q and r are integers, f(0) and f(-1) are odd integers. Which of the following is/are CORRECT ?

(A) f(1) is an even integer

(B) f(1) is an odd integer

(C) f(x) = 0 has three distinct integer roots

(D) f(x) = 0 cannot have three integer roots