K 2K Game

Interview

Time limit1sMemory limit256 MB

Summary

Print how many integers from 1 to N have a units digit different from both the units digits of K and 2K, then list those integers.

Level: Easy2 of 10
Topics: Implementation, Math, Brute force
Solved: No attempts yet

Problem

To test the concentration of new students, Psychim developed the following simple game.

Two integers $N$ and $K$ are given.
For a positive integer $x$ , let $f(x)$ be the units digit of $x$ . You say all integers $x$ with $1 \le x \le N$ such that $f(x) \neq f(K)$ and $f(x) \neq f(2K)$ , in increasing order.

Since you find it tedious to work out units digits one by one, you decide to write a program in secret to win the game. Write a program that prints the full list of numbers you must say.

Input

Two integers $N$ and $K$ are given, separated by a space.

Output

On the first line, print the count of numbers you must say.

On the second line, print all the numbers you must say on one line. If there are no numbers to say, leave the second line empty. The numbers must be printed in increasing order.

Constraints

$1 \le N, K \le 10^5$

Examples2

Example 1
Input
```
9 4
```
Expected output
```
7
1 2 3 5 6 7 9
```
Example 2
Input
```
16 12
```
Expected output
```
12
1 3 5 6 7 8 9 10 11 13 15 16
```