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
#include <string>
#include <iostream>

using namespace std;

int main()
{
	string S, T;

	cin >> S >> T;

	if (S.size() >= T.size())
	{
		for (int i = 0; i <= S.size() - T.size(); i++)
		{
			if (T[0] == S[i])
			{
				if (T == S.substr(i, T.size()))
				{
					printf("%d\n", i);
				}
			}
		}
	}

	return 0;
}