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 $K! \times (N-K)!$.

Constraints

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

Input

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

N K L

Output

Print the count modulo $998244353$.