XOR World

AtCoder

IDabc121_d

Time2000ms

Memory256MB

Difficulty—

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: * 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. For example, the exclusive OR of $3$ and $5$ is $6$. (When written in base two: the exclusive OR of `011` and `101` is `110`.) ## Constraints * All values in input are integers. * $0 \leq A \leq B \leq 10^{12}$ ## Input Input is given from Standard Input in the following format: $A$ $B$ [samples]

Samples

Input #1

2 4

Output #1

5

$2, 3, 4$ are `010`, `011`, `100` in base two, respectively. The exclusive OR of these is `101`, which is $5$ in base ten.

Input #2

123 456

Output #2

Input #3

123456789012 123456789012

Output #3

123456789012

API Response (JSON)

{
  "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"
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  "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* ...",
      "is_translate": false,
      "language": "English"
    }
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}

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