Smaller XOR

AtCoder

IDarc129_a

Time2000ms

Memory256MB

Difficulty—

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 $\mathrm{XOR}$.） What is the bitwise $\mathrm{XOR}$?The bitwise $\mathrm{XOR}$ of integers $A$ and $B$, $A\oplus B$, is defined as follows: * 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. For example, we have $3\oplus 5 = 6$ (in base two: $011\oplus 101 = 110$). ## Constraints * $1 \leq N \leq 10^{18}$ * $1 \leq L \leq R \leq 10^{18}$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $L$ $R$ [samples]

Samples

Input #1

2 1 2

Output #1

1

For $x=1$, $L \leq x \leq R$ 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.

Input #2

10 2 19

Output #2

Input #3

1000000000000000000 1 1000000000000000000

Output #3

847078495393153025

API Response (JSON)

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

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