Lunlun Number

AtCoder

IDabc161_d

Time2000ms

Memory256MB

Difficulty—

A positive integer $X$ is said to be a lunlun number if and only if the following condition is satisfied: * In the base ten representation of $X$ (without leading zeros), for every pair of two adjacent digits, the absolute difference of those digits is at most $1$. For example, $1234$, $1$, and $334$ are lunlun numbers, while none of $31415$, $119$, or $13579$ is. You are given a positive integer $K$. Find the $K$\-th smallest lunlun number. ## Constraints * $1 \leq K \leq 10^5$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $K$ [samples]

Samples

Input #1

Output #1

23

We will list the $15$ smallest lunlun numbers in ascending order:  
$1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $10$, $11$, $12$, $21$, $22$, $23$.  
Thus, the answer is $23$.

Input #2

Output #2

Input #3

Output #3

Input #4

Output #4

3234566667

Note that the answer may not fit into the $32$\-bit signed integer type.

API Response (JSON)

{
  "problem": {
    "name": "Lunlun Number",
    "description": {
      "content": "A positive integer $X$ is said to be a lunlun number if and only if the following condition is satisfied: *   In the base ten representation of $X$ (without leading zeros), for every pair of two adja",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc161_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "A positive integer $X$ is said to be a lunlun number if and only if the following condition is satisfied:\n\n*   In the base ten representation of $X$ (without leading zeros), for every pair of two adja...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments