{"raw_statement":[{"iden":"problem statement","content":"A sequence $S$ of non-negative integers is said to be a **good sequence** if:\n\n*   there exists a non-empty (not necessarily contiguous) subsequence $T$ of $S$ such that the bitwise XOR of all elements in $T$ is $1$.\n\nThere are an empty sequence $A$, and $2^B$ cards with each of the integers between $0$ and $2^B-1$ written on them.  \nYou repeat the following operation until $A$ becomes a good sequence:\n\n*   You freely choose a card and append the integer written on it to the tail of $A$. Then, you eat the card. (Once eaten, the card cannot be chosen anymore.)\n\nHow many sequences of length $N$ can be the final $A$ after the operations? Find the count modulo $998244353$.\nWhat is bitwise XOR? The bitwise $\\mathrm{XOR}$ of non-negative integers $A$ and $B$, $A \\oplus B$, is defined as follows.\n\n*   When $A \\oplus B$ is written in binary, the $k$\\-th lowest bit ($k \\geq 0$) is $1$ if exactly one of the $k$\\-th lowest bits of $A$ and $B$ is $1$, and $0$ otherwise.\n\nFor instance, $3 \\oplus 5 = 6$ (in binary: $011 \\oplus 101 = 110$)."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq B \\leq 10^7$\n*   $N \\leq 2^B$\n*   $N$ and $B$ are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $B$"},{"iden":"sample input 1","content":"2 2"},{"iden":"sample output 1","content":"5\n\nThe following five sequences of length $2$ can be the final $A$ after the operations.\n\n*   $(0, 1)$\n*   $(2, 1)$\n*   $(2, 3)$\n*   $(3, 1)$\n*   $(3, 2)$"},{"iden":"sample input 2","content":"2022 1119"},{"iden":"sample output 2","content":"293184537"},{"iden":"sample input 3","content":"200000 10000000"},{"iden":"sample output 3","content":"383948354"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}