To Infinity

AtCoder

IDabc106_c

Time2000ms

Memory256MB

Difficulty—

Mr. Infinity has a string $S$ consisting of digits from `1` to `9`. Each time the date changes, this string changes as follows: * Each occurrence of `2` in $S$ is replaced with `22`. Similarly, each `3` becomes `333`, `4` becomes `4444`, `5` becomes `55555`, `6` becomes `666666`, `7` becomes `7777777`, `8` becomes `88888888` and `9` becomes `999999999`. `1` remains as `1`. For example, if $S$ is `1324`, it becomes `1333224444` the next day, and it becomes `133333333322224444444444444444` the day after next. You are interested in what the string looks like after $5 \times 10^{15}$ days. What is the $K$\-th character from the left in the string after $5 \times 10^{15}$ days? ## Constraints * $S$ is a string of length between $1$ and $100$ (inclusive). * $K$ is an integer between $1$ and $10^{18}$ (inclusive). * The length of the string after $5 \times 10^{15}$ days is at least $K$. ## Input Input is given from Standard Input in the following format: $S$ $K$ [samples]

Samples

Input #1

1214
4

Output #1

2

The string $S$ changes as follows:

*   Now: `1214`
*   After one day: `12214444`
*   After two days: `1222214444444444444444`
*   After three days: `12222222214444444444444444444444444444444444444444444444444444444444444444`

The first five characters in the string after $5 \times 10^{15}$ days is `12222`. As $K=4$, we should print the fourth character, `2`.

Input #2

3
157

Output #2

3

The initial string is `3`. The string after $5 \times 10^{15}$ days consists only of `3`.

Input #3

299792458
9460730472580800

Output #3

API Response (JSON)

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  "problem": {
    "name": "To Infinity",
    "description": {
      "content": "Mr. Infinity has a string $S$ consisting of digits from `1` to `9`. Each time the date changes, this string changes as follows: *   Each occurrence of `2` in $S$ is replaced with `22`. Similarly, eac",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc106_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Mr. Infinity has a string $S$ consisting of digits from `1` to `9`. Each time the date changes, this string changes as follows:\n\n*   Each occurrence of `2` in $S$ is replaced with `22`. Similarly, eac...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments