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Z Algorithm For Pattern Searching

1. You are given two strings s1 and s2. 2. s1 represents a text and s2 represents a pattern. 3. You have to print the starting index for all occurrences of the pattern in the given text string.

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Z Algorithm For Pattern Searching

hard

1. You are given two strings s1 and s2. 2. s1 represents a text and s2 represents a pattern. 3. You have to print the starting index for all occurrences of the pattern in the given text string.

Constraints

1 <= length of the strings <= 10^4

Format

Input

Two strings s1 and s2 in two different lines.

Output

Starting index for all occurrences of the pattern in the given text string.

Example

Sample Input

abab ab

Sample Output

0 2

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