{"raw_statement":[{"iden":"problem statement","content":"There are $N$ coins numbered $1, 2, \\ldots, N$ arranged in a row. Initially, all coins face up.\nSnuke chooses a permutation $p$ of $(1,\\ldots,N)$ with equal probability, and do $N$ operations. The $i$\\-th operation does the following.\n\n*   If the coin numbered $i$ faces down, do nothing.\n*   If the coin numbered $i$ faces up, turn that coin over and then turn over the coin numbered $p_i$.\n\nAfter the $N$ operations, Snuke will receive $W^k$ yen (Japanese currency) from his mother, where $k$ is the number of coins facing up.\nFind the expected value of the amount Snuke will get, multiplied by $N!$ (it can be proved that this is an integer), modulo $998244353$."},{"iden":"constraints","content":"*   All values in input are integers.\n*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq W < 998244353$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $W$"},{"iden":"sample input 1","content":"4 2"},{"iden":"sample output 1","content":"90\n\n*   When $p=(1,4,2,3)$, the operations go as follows.\n    *   In the $1$\\-st operation, the coin numbered $1$ faces down, and then the coin numbered $1$ faces up.\n    *   In the $2$\\-nd operation, the coin numbered $2$ faces down, and then the coin numbered $4$ faces down.\n    *   In the $3$\\-rd operation, the coin numbered $3$ faces down, and then the coin numbered $2$ faces up.\n    *   In the $4$\\-th operation, nothing is done.\n*   In the end, two coins face up, so he receives $4$ yen."},{"iden":"sample input 2","content":"2 100"},{"iden":"sample output 2","content":"10001"},{"iden":"sample input 3","content":"200000 12345"},{"iden":"sample output 3","content":"541410753\n\n*   Be sure to find the value modulo $998244353$."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}