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 <iostream>
#include <cstdio>
#include <string>

using namespace std;

void solve()
{
	string T, P;
	cin >> T >> P;
	int size = T.size() - P.size() + 1;
	for (int i = 0; i < size; ++i)
	{
		i = T.find(P, i);
		if (i != string::npos)
		{
			printf("%d\n", i);
		}
		else
		{
			return;
		}
	}
}

int main()
{
	solve();
	return(0);
}