Problem Statement

How many integer sequences $A=(A_1,\\ldots,A_N)$ of length $N$ satisfy all the conditions below?

• $1\\le A_i \\le M$ $(1 \\le i \\le N)$

• $|A_i - A_{i+1}| \\geq K$ $(1 \\le i \\le N - 1)$

Since the count can be enormous, find it modulo $998244353$.

Constraints

• $2 \\leq N \\leq 1000$
• $1 \\leq M \\leq 5000$
• $0 \\leq K \\leq M-1$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$ $K$

Output

Print the count modulo $998244353$.

Sample Input 1

2 3 1

Sample Output 1

6

The following $6$ sequences satisfy the conditions.

• $(1,2)$
• $(1,3)$
• $(2,1)$
• $(2,3)$
• $(3,1)$
• $(3,2)$

Sample Input 2

3 3 2

Sample Output 2

2

The following $2$ sequences satisfy the conditions.

• $(1,3,1)$
• $(3,1,3)$

Sample Input 3

100 1000 500

Sample Output 3

657064711

Print the count modulo $998244353$.