Problem:
Score : 400 points

Problem Statement

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

Output

Print the answer.

Sample Input 1

15

Sample 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.

Sample Input 2

1

Sample Output 2

1

Sample Input 3

13

Sample Output 3

21

Sample Input 4

100000

Sample Output 4

3234566667

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

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

namespace AtCoder
{
    class Program
    {
        static List<string> lunlun;
        static Dictionary<string, List<string>> digits;

        static void Main(string[] args)
        {
            //[summary]D - Lunlun Number
            int K = int.Parse(Console.ReadLine());

            if (K < 10)
            {
                Console.WriteLine(K);
            }
            else
            {
                //1ケタのルンルン数(1～9)をListに追加
                GetFirstDigit();

                //各ケタの数字の右隣に来る可能性のある数字をリストアップ
                //(隣り合うどの2つの桁の値についても、差の絶対値が1以下)
                GetDigits();

                Console.WriteLine(GetLunLunNumber(K));
            }            
        }

        static string GetLunLunNumber(int K)
        {
            var count = lunlun.Count;

            while (true)
            {
                var copy = new List<string>(lunlun);
                lunlun.Clear();

                foreach (var c in copy)
                {
                    var key = c.Substring(c.Length - 1, 1);

                    foreach (var d in digits[key])
                    {
                        lunlun.Add(c + d);

                        count++;

                        if (count == K)
                        {
                            return c + d;
                        }
                    }
                }
            }
        }

        static void GetDigits()
        {
            digits = new Dictionary<string, List<string>>();

            for (int i = 0; i <= 9; i++)
            {
                var values = new List<string>();

                for (int j = -1; j <= 1; j++)
                {
                    if (i + j >= 0 && i + j <= 9)
                    {
                        values.Add((i + j).ToString());
                    }
                }

                digits.Add(i.ToString(), values);
            }
        }

        static void GetFirstDigit()
        {
            lunlun = new List<string>();

            for (int i = 1; i <= 9; i++)
            {
                lunlun.Add(i.ToString());
            }
        }
    }
}