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
# -*- coding: utf-8 -*-
import sys


def main():
    inputStr = sys.stdin.read()
    lines = inputStr.split("\n")
    text, word = lines[0], lines[1]
    word_length = len(word)
    for i in range(len(text) - word_length + 1):
        if word == text[i:(i + word_length)]:
            print(i)


if __name__ == '__main__':
    main()

