{"problem":{"name":"Sequence 2","description":{"content":"Consider integer sequences $A=(a_1,a_2,\\dots,a_N)$ of length $N$, where each element is a non-negative integer not greater than $M$.   Count how many such sequences satisfy the following condition, an","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"fps_24_d"},"statements":[{"statement_type":"Markdown","content":"Consider integer sequences $A=(a_1,a_2,\\dots,a_N)$ of length $N$, where each element is a non-negative integer not greater than $M$.  \nCount how many such sequences satisfy the following condition, and output the result modulo $998244353$.\n\n*   Let $B=(b_1,b_2,\\dots,b_N)$ be the sequence obtained by sorting $A$ in ascending order.  \n    For every $i$ such that $1 \\leq i \\leq N-1$, the parity of $b_i$ and $b_{i+1}$ must be different.\n\n## Constraints\n\n*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq M \\leq 2 \\times 10^5$\n*   $N, M$ are integers\n\n## Input\n\nThe input is given from standard input in the following format:\n\n$N$ $M$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"fps_24_d","tags":[],"sample_group":[["2 3","8\n\nThere are $8$ sequences that satisfy the condition:\n\n*   $(0,1)$\n*   $(0,3)$\n*   $(1,0)$\n*   $(1,2)$\n*   $(2,1)$\n*   $(2,3)$\n*   $(3,0)$\n*   $(3,2)$"],["12345 67890","761484871"]],"created_at":"2026-03-03 11:01:14"}}