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
def main():
    T, P = input(), input()
    t, p = len(T), len(P)
    if t>=p:
        ans = [str(n) for n, i in enumerate(range(p, t+1)) if T[n:i]==P]
        if ans:
            print("\n".join(ans))

if __name__ == "__main__":
    main()
