{"problem":{"name":"Ex - make 1","description":{"content":"A sequence $S$ of non-negative integers is said to be a **good sequence** if: *   there exists a non-empty (not necessarily contiguous) subsequence $T$ of $S$ such that the bitwise XOR of all element","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":3000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc278_h"},"statements":[{"statement_type":"Markdown","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: $011 \\oplus 101 = 110$).\n\n## Constraints\n\n*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq B \\leq 10^7$\n*   $N \\leq 2^B$\n*   $N$ and $B$ are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$ $B$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc278_h","tags":[],"sample_group":[["2 2","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*   $(3, 2)$"],["2022 1119","293184537"],["200000 10000000","383948354"]],"created_at":"2026-03-03 11:01:13"}}