AT_arc228_a [ARC228A] Row and Col swap

You are given permutations $ P=(P_1,P_2,\dots,P_N) $ and $ Q=(Q_1,Q_2,\dots,Q_N) $ of $ (1,2,\dots,N) $ . For $ P $ and $ Q $ , you repeat the following $ M $ times: choose and perform one of the operations below. - Choose integers $ i $ and $ j $ satisfying $ 1 \le i < j \le N $ , and swap $ P_i $ and $ P_j $ . - Choose integers $ i $ and $ j $ satisfying $ 1 \le i < j \le N $ , and swap $ Q_i $ and $ Q_j $ . - Choose an integer $ i $ satisfying $ 1 \le i \le N $ , and swap $ P_i $ and $ Q_i $ . Find the number, modulo $ 998244353 $ , of sequences of operations such that both $ P $ and $ Q $ are permutations of $ (1,2,\dots,N) $ after the $ M $ operations.

The input is given from Standard Input in the following format: > $ N $ $ M $ $ P_1\ P_2\ \dots\ P_N $ $ Q_1\ Q_2\ \dots\ Q_N $

Output the answer.

### Sample Explanation 1 For example, the following sequence of operations satisfies the condition. - Choose $ i = 1 $ in an operation of the third kind to swap $ P_1 $ and $ Q_1 $ . Now $ P=(1,2,3) $ and $ Q=(1,3,2) $ . Any sequence of operations composed of exactly one of the following seven operations satisfies the condition: the three operations that swap two elements of $ P $ , the three operations that swap two elements of $ Q $ , and the operation described above that swaps $ P_1 $ and $ Q_1 $ . ### Constraints - $ 1 \le N,M \le 500 $ - $ P $ and $ Q $ are permutations of $ (1,2,\dots,N) $ . - All input values are integers.