Inexact match

Given two strings, (p) and (t), your task is to find all occurrences of (p) within (t) as a substring, allowing for at most one character mismatch.

Input

The first line of the input contains the string (p), and the second line contains the string (t). The lengths of (p) and (t) satisfy (1 $\le$ |p|, |t| $\le$ 10^6). Both strings consist of letters from the Latin alphabet.

Output

On the first line, print the number of times (p) appears in (t) with at most one character mismatch. On the second line, print the starting positions of these occurrences in (t) in ascending order. The positions should be numbered starting from one.

Examples