A probability problem by Áron Bán-Szabó

A : The number of ways that we can choose maximum $M$ number of positive integers, the sum of which is $N$ .

B : The number of ways that we can choose exactly $M$ distinct positive integers, the sum of which is $N+\dfrac{M(M+1)}{2}.$

Which is bigger, A or B?

Note: M and N are positive integers. The order of the chosen numbers (in both cases) doesn't count.