AT_arc212_c [ARC212C] ABS Ball

There are $ N $ white balls. First, you paint each ball red or blue. Then, you place these $ N $ red or blue painted balls in one of $ M $ distinguishable boxes. Let $ a_i $ and $ b_i $ be the number of red and blue balls in the $ i $ -th box, respectively. Find the sum, modulo $ 998244353 $ , of $ \prod_{1\leq i \le M}|a_i-b_i| $ over all ways to place the balls. Here, two ways of placing balls are different if and only if at least one of $ a_i $ and $ b_i $ is different for some $ i $ . Particularly, **balls are not distinguished from each other**.

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

Output the answer.

### Sample Explanation 1 There are three ways to place balls in box $ 1 $ . If you place one red ball and one blue ball, $ |a_1-b_1|=0 $ . If you place two red balls or two blue balls, $ |a_1-b_1|=2 $ . Therefore, the answer is $ 0 + 2 + 2 = 4 $ . ### Constraints - $ 1 \le N,M \le 10^7 $ - All input values are integers.