{"raw_statement":[{"iden":"problem statement","content":"Consider a sequence of integer sets of length $N$: $S=(S_1,S_2,\\dots,S_N)$. We call a sequence **brilliant** if it satisfies all of the following conditions:\n\n*   $S_i$ is a (possibly empty) integer set, and its elements are in the range $[1,M]$. $(1 \\le i \\le N)$\n    \n*   The number of integers that is included in exactly one of $S_i$ and $S_{i+1}$ is $1$. $(1 \\le i \\le N-1)$\n    \n\nWe define the score of a brilliant sequence $S$ as $\\displaystyle \\prod_{i=1}^{M}$ $($ the number of sets among $S_1,S_2,\\dots,S_N$ that include $i$.$)$.\nFind, modulo $998244353$, the sum of the scores of all possible brilliant sequences."},{"iden":"constraints","content":"*   $1 \\le N,M \\le 2 \\times 10^5$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$"},{"iden":"sample input 1","content":"2 3"},{"iden":"sample output 1","content":"24\n\nAmong all possible brilliant sequences, the following $6$ have positive scores.\n\n*   $S_1={1,2},S_2={1,2,3}$\n*   $S_1={1,3},S_2={1,2,3}$\n*   $S_1={2,3},S_2={1,2,3}$\n*   $S_1={1,2,3},S_2={1,2}$\n*   $S_1={1,2,3},S_2={1,3}$\n*   $S_1={1,2,3},S_2={2,3}$\n\nAll of them have a score of $4$, so the sum of them is $24$."},{"iden":"sample input 2","content":"12 34"},{"iden":"sample output 2","content":"786334067"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}