Two lines

Given two strings, A and B, your task is to find all the positions where string B appears as a substring within string A.

Input

The first line of input contains the string A with a length between 1 and 10^5. The second line contains the string B, also with a length between 1 and 10^5.

Output

On the first line, print the total number of times string B occurs as a substring in string A. On the second line, print the starting positions of each occurrence in ascending order, separated by spaces. Follow the format shown in the example for input and output.

Examples