Base -2 Number

AtCoder

IDabc105_c

Time2000ms

Memory256MB

Difficulty—

Given an integer $N$, find the base $-2$ representation of $N$. Here, $S$ is the base $-2$ representation of $N$ when the following are all satisfied: * $S$ is a string consisting of `0` and `1`. * Unless $S =$ `0`, the initial character of $S$ is `1`. * Let $S = S_k S_{k-1} ... S_0$, then $S_0 \times (-2)^0 + S_1 \times (-2)^1 + ... + S_k \times (-2)^k = N$. It can be proved that, for any integer $M$, the base $-2$ representation of $M$ is uniquely determined. ## Constraints * Every value in input is integer. * $-10^9 \leq N \leq 10^9$ ## Input Input is given from Standard Input in the following format: $N$ [samples]

Samples

Input #1

\-9

Output #1

1011

As $(-2)^0 + (-2)^1 + (-2)^3 = 1 + (-2) + (-8) = -9$, `1011` is the base $-2$ representation of $-9$.

Input #2

123456789

Output #2

11000101011001101110100010101

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Base -2 Number",
    "description": {
      "content": "Given an integer $N$, find the base $-2$ representation of $N$. Here, $S$ is the base $-2$ representation of $N$ when the following are all satisfied: *   $S$ is a string consisting of `0` and `1`. *",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc105_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given an integer $N$, find the base $-2$ representation of $N$.\nHere, $S$ is the base $-2$ representation of $N$ when the following are all satisfied:\n\n*   $S$ is a string consisting of `0` and `1`.\n*...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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