Given a Current Stock Price $S$ , Strike Price $K$ , and Barrier

Given a current stock price $S$ , strike price $K$ , and barrier $H$ , which of the following statements is most valid?

A) Given $H < K < S$ , if the barrier $H$ is moved lower, then a down-and-in put increases in value and a down-and-out put falls in value.
B) Given $H < S < K$ , if the barrier $H$ is moved lower, then a down-and-in put and a down-and-out put both increase in value.
C) Given $H < K < S$ , if the barrier $H$ is moved lower, then a down-and-out call increases in value and a down-and-in call decreases in value.
D) Given $H < K < S$ , if the barrier $H$ is moved lower, then a down-and-out call and a down-and-in call both increase in value.