Problem Statement

You are given integers $N,M,X$.

Perform the following series of operations to create a sequence $A$ of length $N$ consisting of non-negative integers.

• Freely decide an integer sequence $A=(A_1,A_2)$ of length $2$.
• Then, perform the following operation $N-2$ times on $A$.

A sequence $A$ is a good sequence if and only if it satisfies the following:

• $0 \le A_i \le M \ (1 \le i \le N)$
• $A_N=X$

Find the sum, modulo $998244353$, of $A_1 \times A_2$ over all good sequences that can be obtained by the operations.

Constraints

• $3 \leq N \leq 2 \times 10^5$
• $1 \leq X \leq M \leq 2 \times 10^5$
• All input values are integers.

Input

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

N M X

Output

Output the answer.