{"raw_statement":[{"iden":"problem statement","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: $011 \\oplus 101 = 110$)."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 200$\n*   $0 \\leq M \\lt 2^{30}$\n*   $0 \\leq X \\lt 2^{30}$\n*   All values in the input are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $M$ $X$"},{"iden":"sample input 1","content":"3 3 2"},{"iden":"sample output 1","content":"5\n\nHere are the five sequences of length $N$ that satisfy both conditions in the statement: $(0, 0, 2), (0, 1, 3), (1, 1, 2), (2, 2, 2), (2, 3, 3)$."},{"iden":"sample input 2","content":"200 900606388 317329110"},{"iden":"sample output 2","content":"788002104"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}