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.

Input

Input is given from Standard Input in the following format:
N M K

Output

Print the count 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.

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.

见题面 Input 部分

见题面 Output 部分