Score : $300$ points

问题陈述

在以10进制表示的正整数中，仅包含数字0和2的那些数中，找出第K小的整数。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Among the positive integers that consist of $0$'s and $2$'s when written in base $10$, find the $K$-th smallest integer.

Constraints

• $K$ is an integer between $1$ and $10^{18}$ (inclusive).

Input

Input is given from Standard Input in the following format:

$K$

Output

Print the answer as an integer.
Here, the exact value must be printed as an integer, even if it is big. Exponential notations such as 2.34e+22, for example, or unnecessary leading zeros such as 0523 are not allowed.

Sample Input 1

3

Sample Output 1

22

The positive integers that consist of $0$'s and $2$'s when written in base $10$ are $2,20,22,\dots$ in ascending order.
The $(K=)$ $3$-rd of them, which is $22$, should be printed.

Sample Input 2

11

Sample Output 2

2022

Sample Input 3

923423423420220108

Sample Output 3

220022020000202020002022022000002020002222002200002022002200

Note that the exact value of the answer must be printed as an integer, even if it is big.

update @ 2024/3/10 10:09:56