#AT1774. F - Cube
F - Cube
F - Cube
Score : $600$ points
Problem Statement
Let us write a positive integer on each face of a cube. How many ways are there to do this so that the sum of the six numbers written is $S$?
Here, two ways to write numbers are not distinguished when they only differ by rotation. (Numbers have no direction.)
The count can be enormous, so find it modulo $998244353$.
Constraints
- $6 \leq S \leq 10^{18}$
- $S$ is an integer.
Input
Input is given from Standard Input in the following format:
Output
Print the count modulo $998244353$.
8
3
We have one way to write $1,1,1,1,1,3$ on the cube and two ways to write $1,1,1,1,2,2$ (one where we write $2$ on adjacent faces and another where we write $2$ on opposite faces), for a total of three ways.
9
5
50
80132
10000000000
2239716
Find the count modulo $998244353$.