{"problem":{"name":"Ex - A Nameless Counting Problem","description":{"content":"Print the number of integer sequences of length $N$, $A = (A_1, A_2, \\ldots, A_N)$, that satisfy both of the following conditions, modulo $998244353$. *   $0 \\leq A_1 \\leq A_2 \\leq \\cdots \\leq A_N \\l","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":3000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc288_h"},"statements":[{"statement_type":"Markdown","content":"Print the number of integer sequences of length $N$, $A = (A_1, A_2, \\ldots, A_N)$, that satisfy both of the following conditions, modulo $998244353$.\n\n*   $0 \\leq A_1 \\leq A_2 \\leq \\cdots \\leq A_N \\leq M$\n*   $A_1 \\oplus A_2 \\oplus \\cdots \\oplus A_N = X$\n\nHere, $\\oplus$ denotes bitwise XOR.\nWhat is bitwise XOR?The bitwise 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*   $1 \\leq N \\leq 200$\n*   $0 \\leq M \\lt 2^{30}$\n*   $0 \\leq X \\lt 2^{30}$\n*   All values in the input are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$ $M$ $X$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc288_h","tags":[],"sample_group":[["3 3 2","5\n\nHere are the five sequences of length $N$ that satisfy both conditions in the statement: $(0, 0, 2), (0, 1, 3), (1, 1, 2), (2, 2, 2), (2, 3, 3)$."],["200 900606388 317329110","788002104"]],"created_at":"2026-03-03 11:01:14"}}