Maija has created herself a text editor that she has nicked Vimm - Vim improved. Now she needs a way to implement the Ctrl-F functionality: find all strings that match the searched string. As a part of this program she will write a function that returns all the positions where string $a$ occurs in string $b$. Position $1$ is the first character of $b$.

Input

A single line contains two string $a$ and $b$, separated by space.

Output

First print the number of positions and then in the next line print the positions where and occurrence of string $a$ starts in string $b$ in increasing order. The strings are 1-indexed.

Constraints

• $1 \leq |a| \leq |b| \leq 2 \times 10^5$
• $a$ and $b$ consist of lowercase Latin letters.

Example 1

Input:

bbb babbabbbbb

Output:

3
6 7 8

Example 2

Input:

l uilzslziog

Output:

2
3 6