If A is poi(1) and B is a poi(2), and both are independent random variables

1. Find the possible values of A if A+B= 100?

2. Get P(A = j | A+ B= 100) for all possible j's (I believe the equation solution is (100!/(1+2)^100)*((1^j * 2^(400-j) )/ j!(100-j)!), but not sure how to get to it