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;

int main(){
	int tl,pl;
	string T,P;

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