{"raw_statement":[{"iden":"problem statement","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 $1 \\leq j \\leq N$."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 10^5$\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."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $S$\n$A_1$ $\\ldots$ $A_N$"},{"iden":"sample input 1","content":"3 7\n2 4 5"},{"iden":"sample output 1","content":"3\n\nThe following three sequences satisfy the conditions.\n\n*   $(1, 5, 1)$\n*   $(3, 3, 1)$\n*   $(7)$"},{"iden":"sample input 2","content":"5 60\n10 20 30 40 50"},{"iden":"sample output 2","content":"37634180"},{"iden":"sample input 3","content":"10 1000000000000000000\n1 2 4 8 16 32 64 128 256 512"},{"iden":"sample output 3","content":"75326268"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}