Score : 1200 points
In Republic of AtCoder, Snuke Chameleons (Family: Chamaeleonidae, Genus: Bartaberia) are very popular pets. Ringo keeps N Snuke Chameleons in a cage.
A Snuke Chameleon that has not eaten anything is blue. It changes its color according to the following rules:
Initially, every Snuke Chameleon had not eaten anything. Ringo fed them by repeating the following process K times:
After Ringo threw in K balls, all the chameleons were red. We are interested in the possible ways Ringo could have thrown in K balls. How many such ways are there? Find the count modulo 998244353. Here, two ways to throw in balls are considered different when there exists i such that the color of the ball that are thrown in the i-th throw is different.
Input is given from Standard Input in the following format:
N K
Print the possible ways Ringo could have thrown in K balls, modulo 998244353.
2 4
7
We will use R
to represent a red ball, and B
to represent a blue ball. There are seven ways to throw in balls that satisfy the condition: BRRR
, RBRB
, RBRR
, RRBB
, RRBR
, RRRB
and RRRR
.
3 7
57
8 3
0
8 10
46
123456 234567
857617983