Base n

AtCoder

IDabc192_d

Time2000ms

Memory256MB

Difficulty—

Given are a string $X$ consisting of `0` through `9`, and an integer $M$. Let $d$ be the greatest digit in $X$. How many different integers not greater than $M$ can be obtained by choosing an integer $n$ not less than $d+1$ and seeing $X$ as a base-$n$ number? ## Constraints * $X$ consists of `0` through `9`. * The length of $X$ is between $1$ and $60$ (inclusive). * $X$ does not begin with a `0`. * $1 \leq M \leq 10^{18}$ ## Input Input is given from Standard Input in the following format: $X$ $M$ [samples]

Samples

Input #1

22
10

Output #1

2

The greatest digit in $X$ is `2`.

*   By seeing $X$ as a base-$3$ number, we get $8$.
*   By seeing $X$ as a base-$4$ number, we get $10$.

These two values are the only ones that we can obtain and are not greater than $10$.

Input #2

999
1500

Output #2

3

The greatest digit in $X$ is `9`.

*   By seeing $X$ as a base-$10$ number, we get $999$.
*   By seeing $X$ as a base-$11$ number, we get $1197$.
*   By seeing $X$ as a base-$12$ number, we get $1413$.

These three values are the only ones that we can obtain and are not greater than $1500$.

Input #3

100000000000000000000000000000000000000000000000000000000000
1000000000000000000

Output #3

1

By seeing $X$ as a base-$2$ number, we get $576460752303423488$, which is the only value that we can obtain and are not greater than $1000000000000000000$.

API Response (JSON)

{
  "problem": {
    "name": "Base n",
    "description": {
      "content": "Given are a string $X$ consisting of `0` through `9`, and an integer $M$. Let $d$ be the greatest digit in $X$. How many different integers not greater than $M$ can be obtained by choosing an integer ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc192_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given are a string $X$ consisting of `0` through `9`, and an integer $M$.\nLet $d$ be the greatest digit in $X$.\nHow many different integers not greater than $M$ can be obtained by choosing an integer ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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