Problem Statement

The AtCoder language has L different characters.
How many N-character strings s consisting of characters in the AtCoder language satisfy the following condition?
Find the count modulo 998244353.

• All K-character subsequences of the string s are different. More precisely, there are $_N\mathrm{C}_K$ ways to obtain a K-character string by extracting K characters from the string s and concatenating them without changing the order, and all of these ways must generate different strings.

What is $_N\mathrm{C}_K$?$_N\mathrm{C}_K$ refers to the total number of ways to choose K from $N items. More precisely, _N\mathrm{C}_K$ is the value of N! divided by K! $\times (N-K)$!.

Input

The input is given from Standard Input in the following format:
N K L

Output

Print the count modulo 998244353.

Constraints

• $1 \leq K < N \leq 500000$
• $1 \leq L \leq 10^9$
• All input values are integers.

Sample Input 1

4 3 2

Sample Output 1

2

If a and b represent the first and second characters in the language, the condition is satisfied by two strings: abab and baba.

Sample Input 2

100 80 26

Sample Output 2

496798269

Approximately 10^{86} strings satisfy the condition, but here we print the count modulo 998244353, which is 496798269.

Sample Input 3

100 1 26

Sample Output 3

0

Sample Input 4

500000 172172 503746693

Sample Output 4

869120

见题面 Input 部分

见题面 Output 部分