Feeder Robot

Vincent switches his retirement plan from raising horses and goats into raising chickens. He procures $N$ chickens and lays each of them into their own coop (hen house). The coops are placed on a single line numbered sequentially from 1 at the left-most to $N$ at the right-most. To make his retirement blissful (or at least he thought), Vincent buys a feeder robot. This feeder robot is to be loaded with $M$ pellets and it will distribute them for the chickens to feed on. The feeder robot will move from one coop to an adjacent coop and distribute 1 pellet to each coop it visits. If a coop is visited $x$ times by the robot including the robot's initial position, then it will get $x$ pellets. However, Vincent has just noticed that he cannot control how the robot moves. Let the robot be in front of coop $p$. If the robot still has pellets to distribute, it will move to an adjacent coop ($p-1$ or $p+1$) at random and distribute 1 pellet to that coop. This process repeats until the robot has no more pellets to distribute. Note that if $p=1$, then the robot will move to coop 2; similarly, if $p=N$, then the robot will move to coop $N-1$. Since Vincent dislikes you even though you are his only friend, he challenges you to a problem. The challenge is to count how many possible pellets distributions are there if the robot starts at coop $A$. A pellets distribution is defined as a tuple $\langle R, S_{1..N} \rangle$ where $R$ is the final position of the robot and $S_i$ is the number of pellets coop $i$ gets. Two distributions are different if and only if the final position of the robot differs or there is a coop that gets a different number of pellets. The robot's movement or the order when the coop gets a pellet does not matter. Since the output can be quite big, Vincent requires you to give him the non-negative remainder when the output is divided by 998 244 353. Believing that you cannot solve it, Vincent agrees to award you with a hefty reward if you managed to solve his challenge. For example, let $N = 4$, $M = 3$, and $A = 2$. In this example, there are 3 different pellets distributions. $\langle 2, \{1, 2, 0, 0\} \rangle$: The robot ends at coop 2 and the number of pellets each coop gets is $\{1, 2, 0, 0\}$. The robot's movement that causes this distribution is: The robot starts at coop 2 and distributes 1 pellet to coop 2; it moves to coop 1 and distributes 1 pellet to coop 1; it moves to coop 2 and distributes 1 pellet to coop 2. In a simple notation, the robot's movement is 2 → 1 → 2. $\langle 2, \{0, 2, 1, 0\} \rangle$: The robot ends at coop 2 and the number of pellets each coop gets is $\{0, 2, 1, 0\}$. The robot's movement is 2 → 3 → 2. $\langle 4, \{0, 1, 1, 1\} \rangle$: The robot ends at coop 4 and the number of pellets each coop gets is $\{0, 1, 1, 1\}$. The robot's movement is 2 → 3 → 4.

Input contains three integers $N$, $M$, and $A$ (2 ≤ $N$ ≤ 100 000; 1 ≤ $M$ ≤ 200 000; 1 ≤ $A$ ≤ $N$), representing the number of coops, the number of pellets, and the starting position of the feeder robot.

Output contains one integer on a line: the non-negative remainder when the number of different pellets distributions is divided by 998 244 353.