{"problem":{"name":"XOR World","description":{"content":"Let $f(A, B)$ be the exclusive OR of $A, A+1, ..., B$. Find $f(A, B)$. What is exclusive OR? The bitwise exclusive OR of integers $c_1, c_2, ..., c_n$ (let us call it $y$) is defined as follows: * ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc121_d"},"statements":[{"statement_type":"Markdown","content":"Let $f(A, B)$ be the exclusive OR of $A, A+1, ..., B$. Find $f(A, B)$.\n\nWhat is exclusive OR?\n\nThe bitwise exclusive OR of integers $c_1, c_2, ..., c_n$ (let us call it $y$) is defined as follows:\n\n*   When $y$ is written in base two, the digit in the $2^k$'s place ($k \\geq 0$) is $1$ if, the number of integers among $c_1, c_2, ...c_m$ whose binary representations have $1$ in the $2^k$'s place, is odd, and $0$ if that count is even.\n\nFor example, the exclusive OR of $3$ and $5$ is $6$. (When written in base two: the exclusive OR of `011` and `101` is `110`.)\n\n## Constraints\n\n*   All values in input are integers.\n*   $0 \\leq A \\leq B \\leq 10^{12}$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$A$ $B$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc121_d","tags":[],"sample_group":[["2 4","5\n\n$2, 3, 4$ are `010`, `011`, `100` in base two, respectively. The exclusive OR of these is `101`, which is $5$ in base ten."],["123 456","435"],["123456789012 123456789012","123456789012"]],"created_at":"2026-03-03 11:01:14"}}