409067: GYM103428 M 810975

In the platypus kingdom, there is a popular game throughout the kingdom–Hearthstone. Hearthstone consists of eight players in each game, and only one of them wins. Due to the difficulty of winning, many platypuses share their best moments of playing the game via live streams. Recently, a Bible "810975" spread.

"810975, why can't newcomers understand?!"

"810975, why are you the only one who doesn't understand?"

...

Recently, Zayin is reciting the Bible 810975 every day. He also continues to explain to his friends the specific meaning of 810975: On August 10, the Platypus King played 9 games and won 7 times, including a 5-game winning streak. But today, there comes a new platypus, Ziyin, who doesn't know the meaning of 810975. So Zayin excitedly explains to him. However, Ziyin has a question, "How many situations are there if I play $$$n$$$ games and win $$$m$$$ games, and the longest winning streak is $$$k$$$?"

If we use 1 to represent victory and 0 to represent defeat, any string consisting of 0 and 1 of length $$$n$$$ can represent a situation of an $$$n$$$-round game. Two situations are different if and only if the two 01 strings are different.

The first line contains three integers $$$n,m,k$$$ ($$$0 \le n,m,k \le 10^5$$$).

The only line contains an integer: the number of situations meeting the constraints. You should output the answer modulo $$$998244353$$$.

9 7 5

9