Zero or One

AtCoder

IDabc293_f

Time3000ms

Memory256MB

Difficulty—

Given an integer $N$ not less than $2$, find the number of integers $b$ not less than $2$ such that: * when $N$ is written in base $b$, every digit is $0$ or $1$. Find the answer for $T$ independent test cases. It can be proved that there is a finite number of desired integers $b$ not less than $2$ under the constraints of this problem. ## Constraints * $1 \leq T \leq 1000$ * $2 \leq N \leq 10^{18}$ * All values in the input are integers. ## Input The input is given from Standard Input in the following format, where $\mathrm{test}_i$ denotes the $i$\-th test case: $T$ $\mathrm{test}_1$ $\mathrm{test}_2$ $\vdots$ $\mathrm{test}_T$ Each test case is given in the following format: $N$ [samples]

Samples

Input #1

Output #1

4
1
5

For the first test case, four $b$'s satisfy the condition in the problem statement: $b = 2, 3, 11, 12$. Indeed, when $N=12$ is written in base $2, 3, 11$, and $12$, it becomes $1100, 110, 11$ and $10$, respectively.

API Response (JSON)

{
  "problem": {
    "name": "Zero or One",
    "description": {
      "content": "Given an integer $N$ not less than $2$, find the number of integers $b$ not less than $2$ such that: *   when $N$ is written in base $b$, every digit is $0$ or $1$. Find the answer for $T$ independe",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc293_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given an integer $N$ not less than $2$, find the number of integers $b$ not less than $2$ such that:\n\n*   when $N$ is written in base $b$, every digit is $0$ or $1$.\n\nFind the answer for $T$ independe...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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