408065: GYM102978 C Count Min Ratio

You have $$$R$$$ red balls, $$$B$$$ blue balls, and one green ball. You are going to arrange the balls in a row. The score of an arrangement is defined as follows:

• Let $$$l_{\mathrm{R}},l_{\mathrm{B}},r_{\mathrm{R}},r_{\mathrm{B}}$$$ be the number of red/blue balls to the left/right of the green ball, respectively. Then, the score is the maximum integer $$$x$$$ such that $$$l_{\mathrm{B}} \times x \leq l_{\mathrm{R}}$$$ and $$$r_{\mathrm{B}} \times x \leq r_{\mathrm{R}}$$$.

Find the sum of scores of all possible arrangements, modulo $$$998244353$$$. Note that balls of the same color cannot be distinguished, thus two arrangements are considered different if and only if there is such an $$$i$$$ that the color of the $$$i$$$-th ball in the first arrangement differs from that of the second.

The first line contains integers $$$R$$$ ($$$1 \leq R \leq 10^{18}$$$) and $$$B$$$ ($$$1 \leq B \leq 10^6$$$).

Print the answer.

10 3

8390

3 10

0

100 10

801171977

999999999999999999 999999

448294209