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 Rust (1.15.1) (judge verdict: Accepted)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
#![allow(unused_imports)]
#![allow(bare_trait_objects)] // for compatibility with 1.15.1
use std::cmp::Ordering::{self, Greater, Less};
use std::cmp::{max, min};
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
use std::error::Error;
use std::io::{self, BufReader, BufWriter, Read, Write};
use text_scanner::{scan, scan_iter, scanln, scanln_iter};
use utils::adj4_iter;

fn gen(cur: usize, level: usize, output: &mut Vec<usize>) {
    output.push(cur);
    if level == 10 {
        return;
    }
    if cur == 0 {
        for i in 1..10 {
            gen(i, 1, output);
        }
    } else {
        let base = (cur % 10) as i32;
        for i in -1..2 {
            let new = base + i;
            if new >= 0 && new < 10 {
                gen(cur * 10 + new as usize, level + 1, output);
            }
        }
    }
}

fn run() {
    let mut output = Vec::new();
    gen(0, 0, &mut output);
    output.sort();
    let k: usize = scan();
    println!("{}", output[k]);
}

fn main() {
    std::thread::Builder::new()
        .name("run".to_string())
        .stack_size(256 * 1024 * 1024)
        .spawn(run)
        .unwrap()
        .join()
        .unwrap()
}
//{{{ utils
pub mod utils {
    static DY: [isize; 8] = [0, 1, 0, -1, 1, -1, 1, -1];
    static DX: [isize; 8] = [1, 0, -1, 0, 1, 1, -1, -1];

    fn try_adj(
        y: usize,
        x: usize,
        dy: isize,
        dx: isize,
        h: usize,
        w: usize,
    ) -> Option<(usize, usize)> {
        let ny = y as isize + dy;
        let nx = x as isize + dx;
        if ny >= 0 && nx >= 0 {
            let ny = ny as usize;
            let nx = nx as usize;
            if ny < h && nx < w {
                Some((ny, nx))
            } else {
                None
            }
        } else {
            None
        }
    }

    pub struct Adj4 {
        y: usize,
        x: usize,
        h: usize,
        w: usize,
        r: usize,
    }

    impl Iterator for Adj4 {
        type Item = (usize, usize);

        fn next(&mut self) -> Option<Self::Item> {
            loop {
                if self.r >= 4 {
                    return None;
                }

                let dy = DY[self.r];
                let dx = DX[self.r];
                self.r += 1;

                if let Some((ny, nx)) = try_adj(self.y, self.x, dy, dx, self.h, self.w) {
                    return Some((ny, nx));
                }
            }
        }
    }

    pub fn adj4_iter(y: usize, x: usize, h: usize, w: usize) -> Adj4 {
        Adj4 {
            y: y,
            x: x,
            h: h,
            w: w,
            r: 0,
        }
    }
}
pub mod text_scanner {
    use std;
    #[derive(Debug)]
    pub enum Error {
        IoError(std::io::Error),
        EncodingError(std::string::FromUtf8Error),
        ParseError(String),
        Eof,
    }

    impl std::fmt::Display for Error {
        fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
            match *self {
                Error::IoError(ref e) => writeln!(f, "IO Error: {}", e),
                Error::EncodingError(ref e) => writeln!(f, "Encoding Error: {}", e),
                Error::ParseError(ref e) => writeln!(f, "Parse Error: {}", e),
                Error::Eof => writeln!(f, "EOF"),
            }
        }
    }

    impl std::error::Error for Error {
        // dummy implementation for 1.15.1
        fn description(&self) -> &str {
            "description() is deprecated; use Display"
        }
    }

    pub fn read_line() -> Option<String> {
        let stdin = std::io::stdin();
        let mut stdin = stdin.lock();
        fread_line(&mut stdin).expect("IO error")
    }

    pub fn scan<T: FromTokens>() -> T {
        let stdin = std::io::stdin();
        let mut stdin = stdin.lock();
        fscan(&mut stdin).expect("IO error")
    }

    pub fn scanln<T: FromTokens>() -> T {
        let stdin = std::io::stdin();
        let mut stdin = stdin.lock();
        fscanln(&mut stdin).expect("IO error")
    }

    pub fn scan_iter<T: FromTokens>() -> ScanIter<T> {
        ScanIter {
            item_type: std::marker::PhantomData,
        }
    }

    pub fn scanln_iter<T: FromTokens>() -> ScanlnIter<T> {
        let stdin = std::io::stdin();
        let mut stdin = stdin.lock();
        let s = fread_line(&mut stdin)
            .expect("IO error")
            .unwrap_or_else(String::new);
        ScanlnIter {
            cursor: std::io::Cursor::new(s),
            item_type: std::marker::PhantomData,
        }
    }

    pub fn fread_line<R: std::io::BufRead>(r: &mut R) -> Result<Option<String>, std::io::Error> {
        let mut buf = String::new();
        let length = r.read_line(&mut buf)?;
        if let Some('\n') = buf.chars().last() {
            buf.pop();
        }
        if let Some('\r') = buf.chars().last() {
            buf.pop();
        }
        if length == 0 {
            Ok(None)
        } else {
            Ok(Some(buf))
        }
    }

    pub fn fscan<R: std::io::Read, T: FromTokens>(reader: &mut R) -> Result<T, Error> {
        let mut tokenizer = Tokenizer::new(reader);
        FromTokens::from_tokens(&mut tokenizer)
    }

    pub fn fscanln<R: std::io::BufRead, T: FromTokens>(reader: &mut R) -> Result<T, Error> {
        let s = match fread_line(reader) {
            Ok(Some(s)) => s,
            Ok(None) => return Err(Error::Eof),
            Err(e) => return Err(Error::IoError(e)),
        };
        let mut bytes = s.as_bytes();
        let mut tokenizer = Tokenizer::new(&mut bytes);
        FromTokens::from_tokens(&mut tokenizer)
    }

    pub fn fscan_iter<R: std::io::Read, T: FromTokens>(reader: &mut R) -> FscanIter<R, T> {
        FscanIter {
            tokenizer: Tokenizer::new(reader),
            item_type: std::marker::PhantomData,
        }
    }

    pub fn fscanln_iter<R: std::io::BufRead, T: FromTokens>(
        reader: &mut R,
    ) -> Result<ScanlnIter<T>, Error> {
        let s = match fread_line(reader) {
            Ok(Some(s)) => s,
            Ok(None) => "".to_string(),
            Err(e) => return Err(Error::IoError(e)),
        };
        Ok(ScanlnIter {
            cursor: std::io::Cursor::new(s),
            item_type: std::marker::PhantomData,
        })
    }

    pub struct ScanIter<T>
    where
        T: FromTokens,
    {
        item_type: std::marker::PhantomData<T>,
    }

    impl<T: FromTokens> Iterator for ScanIter<T> {
        type Item = T;

        fn next(&mut self) -> Option<Self::Item> {
            let stdin = std::io::stdin();
            let mut stdin = stdin.lock();
            let mut tokenizer = Tokenizer::new(&mut stdin);
            match FromTokens::from_tokens(&mut tokenizer) {
                Err(Error::Eof) => None,
                r => Some(r.expect("IO error")),
            }
        }
    }

    pub struct FscanIter<'a, R, T>
    where
        R: std::io::Read + 'a,
        T: FromTokens,
    {
        tokenizer: Tokenizer<'a, R>,
        item_type: std::marker::PhantomData<T>,
    }

    impl<'a, R: std::io::Read, T: FromTokens> Iterator for FscanIter<'a, R, T> {
        type Item = Result<T, Error>;

        fn next(&mut self) -> Option<Self::Item> {
            match FromTokens::from_tokens(&mut self.tokenizer) {
                Err(Error::Eof) => None,
                r => Some(r),
            }
        }
    }

    pub struct ScanlnIter<T>
    where
        T: FromTokens,
    {
        cursor: std::io::Cursor<String>,
        item_type: std::marker::PhantomData<T>,
    }

    impl<'a, T: FromTokens> Iterator for ScanlnIter<T> {
        type Item = T;

        fn next(&mut self) -> Option<Self::Item> {
            let mut tokenizer = Tokenizer::new(&mut self.cursor);
            match FromTokens::from_tokens(&mut tokenizer) {
                Err(Error::Eof) => None,
                r => Some(r.expect("IO error")),
            }
        }
    }

    pub trait FromTokens
    where
        Self: Sized,
    {
        fn from_tokens(
            tokenizer: &mut Iterator<Item = Result<String, Error>>,
        ) -> Result<Self, Error>;
    }

    macro_rules! from_tokens_primitives {
    ($($t:ty),*) => { $(
        impl FromTokens for $t {
            fn from_tokens(tokenizer: &mut Iterator<Item = Result<String, Error>>) -> Result<Self, Error> {
                let token = tokenizer.next();
                match token {
                    Some(s) => s?
                        .parse::<$t>()
                        .map_err(|e| Error::ParseError(format!("{}", e))),
                    None => Err(Error::Eof),
                }
            }
        }
    )* }
}

    from_tokens_primitives! {
        String,
        bool,
        f32,
        f64,
        isize,
        i8,
        i16,
        i32,
        i64,
        usize,
        u8,
        u16,
        u32,
        u64
    }

    impl FromTokens for Vec<char> {
        fn from_tokens(
            tokenizer: &mut Iterator<Item = Result<String, Error>>,
        ) -> Result<Self, Error> {
            Ok(String::from_tokens(tokenizer)?.chars().collect())
        }
    }

    impl<T1, T2> FromTokens for (T1, T2)
    where
        T1: FromTokens,
        T2: FromTokens,
    {
        fn from_tokens(
            tokenizer: &mut Iterator<Item = Result<String, Error>>,
        ) -> Result<Self, Error> {
            Ok((T1::from_tokens(tokenizer)?, T2::from_tokens(tokenizer)?))
        }
    }

    impl<T1, T2, T3> FromTokens for (T1, T2, T3)
    where
        T1: FromTokens,
        T2: FromTokens,
        T3: FromTokens,
    {
        fn from_tokens(
            tokenizer: &mut Iterator<Item = Result<String, Error>>,
        ) -> Result<Self, Error> {
            Ok((
                T1::from_tokens(tokenizer)?,
                T2::from_tokens(tokenizer)?,
                T3::from_tokens(tokenizer)?,
            ))
        }
    }

    impl<T1, T2, T3, T4> FromTokens for (T1, T2, T3, T4)
    where
        T1: FromTokens,
        T2: FromTokens,
        T3: FromTokens,
        T4: FromTokens,
    {
        fn from_tokens(
            tokenizer: &mut Iterator<Item = Result<String, Error>>,
        ) -> Result<Self, Error> {
            Ok((
                T1::from_tokens(tokenizer)?,
                T2::from_tokens(tokenizer)?,
                T3::from_tokens(tokenizer)?,
                T4::from_tokens(tokenizer)?,
            ))
        }
    }

    impl<T1, T2, T3, T4, T5> FromTokens for (T1, T2, T3, T4, T5)
    where
        T1: FromTokens,
        T2: FromTokens,
        T3: FromTokens,
        T4: FromTokens,
        T5: FromTokens,
    {
        fn from_tokens(
            tokenizer: &mut Iterator<Item = Result<String, Error>>,
        ) -> Result<Self, Error> {
            Ok((
                T1::from_tokens(tokenizer)?,
                T2::from_tokens(tokenizer)?,
                T3::from_tokens(tokenizer)?,
                T4::from_tokens(tokenizer)?,
                T5::from_tokens(tokenizer)?,
            ))
        }
    }

    impl<T1, T2, T3, T4, T5, T6> FromTokens for (T1, T2, T3, T4, T5, T6)
    where
        T1: FromTokens,
        T2: FromTokens,
        T3: FromTokens,
        T4: FromTokens,
        T5: FromTokens,
        T6: FromTokens,
    {
        fn from_tokens(
            tokenizer: &mut Iterator<Item = Result<String, Error>>,
        ) -> Result<Self, Error> {
            Ok((
                T1::from_tokens(tokenizer)?,
                T2::from_tokens(tokenizer)?,
                T3::from_tokens(tokenizer)?,
                T4::from_tokens(tokenizer)?,
                T5::from_tokens(tokenizer)?,
                T6::from_tokens(tokenizer)?,
            ))
        }
    }

    struct Tokenizer<'a, R: std::io::Read + 'a> {
        reader: &'a mut R,
    }

    impl<'a, R: std::io::Read> Tokenizer<'a, R> {
        pub fn new(reader: &'a mut R) -> Self {
            Tokenizer { reader: reader }
        }

        pub fn next_token(&mut self) -> Result<Option<String>, Error> {
            use std::io::Read;
            let mut token = Vec::new();
            for b in self.reader.by_ref().bytes() {
                let b = b.map_err(Error::IoError)?;
                match (is_ascii_whitespace(b), token.is_empty()) {
                    (false, _) => token.push(b),
                    (true, false) => break,
                    (true, true) => {}
                }
            }
            if token.is_empty() {
                return Ok(None);
            }
            String::from_utf8(token)
                .map(Some)
                .map_err(Error::EncodingError)
        }
    }

    impl<'a, R: std::io::Read> Iterator for Tokenizer<'a, R> {
        type Item = Result<String, Error>;
        fn next(&mut self) -> Option<Self::Item> {
            match self.next_token() {
                Ok(Some(s)) => Some(Ok(s)),
                Ok(None) => None,
                Err(e) => Some(Err(e)),
            }
        }
    }

    fn is_ascii_whitespace(b: u8) -> bool {
        // Can use u8::is_ascii_whitespace once removing support of 1.15.1
        match b {
            b'\t' | b'\n' | b'\x0C' | b'\r' | b' ' => true,
            _ => false,
        }
    }
}

pub trait SetMinMax {
    fn set_min(&mut self, v: Self) -> bool;
    fn set_max(&mut self, v: Self) -> bool;
}

impl<T> SetMinMax for T
where
    T: PartialOrd,
{
    fn set_min(&mut self, v: T) -> bool {
        *self > v && {
            *self = v;
            true
        }
    }
    fn set_max(&mut self, v: T) -> bool {
        *self < v && {
            *self = v;
            true
        }
    }
}

#[derive(PartialEq, Eq, Debug, Copy, Clone, Default, Hash)]
pub struct Reverse<T>(pub T);

impl<T: PartialOrd> PartialOrd for Reverse<T> {
    #[inline]
    fn partial_cmp(&self, other: &Reverse<T>) -> Option<Ordering> {
        other.0.partial_cmp(&self.0)
    }

    #[inline]
    fn lt(&self, other: &Self) -> bool {
        other.0 < self.0
    }
    #[inline]
    fn le(&self, other: &Self) -> bool {
        other.0 <= self.0
    }
    #[inline]
    fn ge(&self, other: &Self) -> bool {
        other.0 >= self.0
    }
    #[inline]
    fn gt(&self, other: &Self) -> bool {
        other.0 > self.0
    }
}

impl<T: Ord> Ord for Reverse<T> {
    #[inline]
    fn cmp(&self, other: &Reverse<T>) -> Ordering {
        other.0.cmp(&self.0)
    }
}

#[derive(PartialEq, PartialOrd, Debug, Copy, Clone, Default)]
pub struct Num(pub f64);

impl Eq for Num {}

impl Ord for Num {
    fn cmp(&self, other: &Num) -> Ordering {
        self.0
            .partial_cmp(&other.0)
            .expect("unexpected NaN when compare")
    }
}

// See https://docs.rs/superslice/1.0.0/superslice/trait.Ext.html
pub trait SliceExt {
    type Item;

    fn lower_bound(&self, x: &Self::Item) -> usize
    where
        Self::Item: Ord;

    fn lower_bound_by<'a, F>(&'a self, f: F) -> usize
    where
        F: FnMut(&'a Self::Item) -> Ordering;

    fn lower_bound_by_key<'a, K, F>(&'a self, k: &K, f: F) -> usize
    where
        F: FnMut(&'a Self::Item) -> K,
        K: Ord;

    fn upper_bound(&self, x: &Self::Item) -> usize
    where
        Self::Item: Ord;

    fn upper_bound_by<'a, F>(&'a self, f: F) -> usize
    where
        F: FnMut(&'a Self::Item) -> Ordering;

    fn upper_bound_by_key<'a, K, F>(&'a self, k: &K, f: F) -> usize
    where
        F: FnMut(&'a Self::Item) -> K,
        K: Ord;
}

impl<T> SliceExt for [T] {
    type Item = T;

    fn lower_bound(&self, x: &Self::Item) -> usize
    where
        T: Ord,
    {
        self.lower_bound_by(|y| y.cmp(x))
    }

    fn lower_bound_by<'a, F>(&'a self, mut f: F) -> usize
    where
        F: FnMut(&'a Self::Item) -> Ordering,
    {
        let s = self;
        let mut size = s.len();
        if size == 0 {
            return 0;
        }
        let mut base = 0usize;
        while size > 1 {
            let half = size / 2;
            let mid = base + half;
            let cmp = f(unsafe { s.get_unchecked(mid) });
            base = if cmp == Less { mid } else { base };
            size -= half;
        }
        let cmp = f(unsafe { s.get_unchecked(base) });
        base + (cmp == Less) as usize
    }

    fn lower_bound_by_key<'a, K, F>(&'a self, k: &K, mut f: F) -> usize
    where
        F: FnMut(&'a Self::Item) -> K,
        K: Ord,
    {
        self.lower_bound_by(|e| f(e).cmp(k))
    }

    fn upper_bound(&self, x: &Self::Item) -> usize
    where
        T: Ord,
    {
        self.upper_bound_by(|y| y.cmp(x))
    }

    fn upper_bound_by<'a, F>(&'a self, mut f: F) -> usize
    where
        F: FnMut(&'a Self::Item) -> Ordering,
    {
        let s = self;
        let mut size = s.len();
        if size == 0 {
            return 0;
        }
        let mut base = 0usize;
        while size > 1 {
            let half = size / 2;
            let mid = base + half;
            let cmp = f(unsafe { s.get_unchecked(mid) });
            base = if cmp == Greater { base } else { mid };
            size -= half;
        }
        let cmp = f(unsafe { s.get_unchecked(base) });
        base + (cmp != Greater) as usize
    }

    fn upper_bound_by_key<'a, K, F>(&'a self, k: &K, mut f: F) -> usize
    where
        F: FnMut(&'a Self::Item) -> K,
        K: Ord,
    {
        self.upper_bound_by(|e| f(e).cmp(k))
    }
}
//}}}
*/

fn main() {
    let exe = "/tmp/bin5BB4639B";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";