{"raw_statement":[{"iden":"problem statement","content":"Given are integers $L$, $R$, and $V$. Find the number of pairs of integers $(l,r)$ that satisfy both of the conditions below, modulo $998244353$.\n\n*   $L \\leq l \\leq r \\leq R$\n*   $l \\oplus (l+1) \\oplus \\cdots \\oplus r=V$\n\nHere, $\\oplus$ denotes the bitwise $\\mathrm{XOR}$ operation.\nWhat is bitwise $\\mathrm{XOR}$?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 base two, the digit in the $2^k$'s place ($k \\geq 0$) is $1$ if exactly one of $A$ and $B$ is $1$, and $0$ otherwise.\n\nFor example, we have $3 \\oplus 5 = 6$ (in base two: $011 \\oplus 101 = 110$).  \nGenerally, the bitwise $\\mathrm{XOR}$ of $k$ integers $p_1, p_2, p_3, \\dots, p_k$ is defined as $(\\dots ((p_1 \\oplus p_2) \\oplus p_3) \\oplus \\dots \\oplus p_k)$. We can prove that this value does not depend on the order of $p_1, p_2, p_3, \\dots p_k$."},{"iden":"constraints","content":"*   $1 \\leq L \\leq R \\leq 10^{18}$\n*   $0 \\leq V \\leq 10^{18}$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$L$ $R$ $V$"},{"iden":"sample input 1","content":"1 3 3"},{"iden":"sample output 1","content":"2\n\nThe two pairs satisfying the conditions are $(l,r)=(1,2)$ and $(l,r)=(3,3)$."},{"iden":"sample input 2","content":"10 20 0"},{"iden":"sample output 2","content":"6"},{"iden":"sample input 3","content":"1 1 1"},{"iden":"sample output 3","content":"1"},{"iden":"sample input 4","content":"12345 56789 34567"},{"iden":"sample output 4","content":"16950"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}