AT_arc212_f [ARC212F] Add Integer

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 $ . - Let $ k=|A| $ . Let $ x=A_{k-1}, y=A_k $ . Append either $ x+y $ or $ y-x $ to the end of $ 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.

The input is given from Standard Input in the following format: > $ N $ $ M $ $ X $

Output the answer.

### Sample Explanation 1 Some possible sequences are $ (0,3,3),(1,4,3),(2,1,3) $ . The sum of $ A_1 \times A_2 $ over all possible sequences is $ 8 $ . ### Constraints - $ 3 \leq N \leq 2 \times 10^5 $ - $ 1 \leq X \leq M \leq 2 \times 10^5 $ - All input values are integers.