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

### Output Print the count modulo $998244353$.