{"problem":{"name":"Ex - Odd Steps","description":{"content":"Find the number, modulo $998244353$, of sequences $X$ that satisfy all of the following conditions. *   Every term in $X$ is a positive **odd number**. *   The sum of the terms in $X$ is $S$. *   The","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":3000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc258_h"},"statements":[{"statement_type":"Markdown","content":"Find the number, modulo $998244353$, of sequences $X$ that satisfy all of the following conditions.\n\n*   Every term in $X$ is a positive **odd number**.\n*   The sum of the terms in $X$ is $S$.\n*   The prefix sums of $X$ contain none of $A_1, \\dots, A_N$. Formally, if we define $Y_i = X_1 + \\dots + X_i$ for each $i$, then $Y_i \\neq A_j$ holds for all integers $i$ and $j$ such that $1 \\leq i \\leq |X|$ and $1 \\leq j \\leq N$.\n\n## Constraints\n\n*   $1 \\leq N \\leq 10^5$\n*   $1 \\leq A_1 \\lt A_2 \\lt \\dots \\lt A_N \\lt S \\leq 10^{18}$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $S$\n$A_1$ $\\ldots$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc258_h","tags":[],"sample_group":[["3 7\n2 4 5","3\n\nThe following three sequences satisfy the conditions.\n\n*   $(1, 5, 1)$\n*   $(3, 3, 1)$\n*   $(7)$"],["5 60\n10 20 30 40 50","37634180"],["10 1000000000000000000\n1 2 4 8 16 32 64 128 256 512","75326268"]],"created_at":"2026-03-03 11:01:14"}}