Find places where a string P is found within a text T. Print all indices of T where P found. The indices of T start with 0.

Constraints

• 1 ≤ length of T ≤ 1000000
• 1 ≤ length of P ≤ 10000
• The input consists of alphabetical characters and digits

Input

In the first line, a text T is given. In the second line, a string P is given.

Output

Print an index of T where P found in a line. Print the indices in ascending order.

Examples

Input

aabaaa
aa

Output

0
3
4

Input

xyzz
yz

Output

1

Input

abc
xyz

Output

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