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 <string>
#include <cstdio>
using namespace std;

int main(){
	string T, P;
	cin >> T >> P;
	if (T.size() < P.size()) return 0;
	for (long i = 0; i < T.size() - P.size() + 1; i++){
		if (T[i] == P[0]){
			if (T.substr(i, P.size()) == P) printf("%d\n", i);
		}
	}
	return 0;
}