Problem Statement

Let $N, M, K$ be given integers. Choose $M$ distinct integers from the integers between $1$ and $N$, inclusive.
Let $S$ be the set of chosen numbers, and consider the following condition on $S$.

　Condition: $S$ contains at least $1$ set consisting of $K$ consecutive integers.

Here, for an integer $k$ at least $2$, a set consisting of $k$ consecutive integers refers to a set that can be written as $\{l, l + 1, \cdots\cdots, l + k - 1\}$ using some integer $l$.
For example, $\{1, 2, 3, 5, 7, 8, 9, 10\}$ contains the sets $\{1, 2, 3\}, \{7, 8, 9\}, \{8, 9, 10\}$, each consisting of $3$ consecutive integers.

How many ways of choosing satisfy the condition? Output this number of ways modulo $998244353$ to the answer file.

Input

$N\ M\ K$

• $2 \leqq K \leqq M \leqq N \leqq 10^7$
• $N, M, K$ are integers.

Output

Output the answer, followed by a newline.

Sample

4 2 2

3

10 5 3

126

10000000 5000000 2021

107056641