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
if __name__ == '__main__':
    # ??????????????\???
    # T = 'abc'
    # P = 'xyz'
    T = input()
    P = input()

    # ???????????????
    results = []

    for i in range(len(T) - len(P) + 1):
        temp = T[i:i+len(P)]
        if temp == P:
            results.append(i)

    # ???????????¨???
    for r in results:
        print(r)