{"problem":{"name":"Smaller XOR","description":{"content":"Given are integers $N$, $L$, and $R$. Count the number of integers $x$ that satisfy both of the following conditions. *   $L \\leq x \\leq R$ *   $(x \\oplus N) < N$ (Here, $\\oplus$ denotes the bitwise ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc129_a"},"statements":[{"statement_type":"Markdown","content":"Given are integers $N$, $L$, and $R$. Count the number of integers $x$ that satisfy both of the following conditions.\n\n*   $L \\leq x \\leq R$\n*   $(x \\oplus N) < N$ (Here, $\\oplus$ denotes the bitwise $\\mathrm{XOR}$.）\n\nWhat is the bitwise $\\mathrm{XOR}$?The bitwise $\\mathrm{XOR}$ of 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: $011\\oplus 101 = 110$).\n\n## Constraints\n\n*   $1 \\leq N \\leq 10^{18}$\n*   $1 \\leq L \\leq R \\leq 10^{18}$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $L$ $R$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc129_a","tags":[],"sample_group":[["2 1 2","1\n\nFor $x=1$, $L \\leq x \\leq R$ is satisfied, but $(x \\oplus N) < N$ is not. For $x=2$, both conditions are satisfied. There is no other $x$ that satisfies the conditions."],["10 2 19","10"],["1000000000000000000 1 1000000000000000000","847078495393153025"]],"created_at":"2026-03-03 11:01:14"}}