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<bits/stdc++.h>
using namespace std;

string T,P;
int FE[10005];

void FuncionError();
void Aparece();

int main(){
	cin>>T;
	cin>>P;
	FuncionError();
	Aparece();
	return 0;
}
void FuncionError(){
	FE[0]=-1;
	for(int i=0;i<P.size();){
		int pos = FE[i];
		while(pos>=0 && (P[pos]!=P[i])){
			pos = FE[pos];
		}
		FE[++i] = ++pos;
	}
}
void Aparece(){
	int pos = 0;
	//cout<<T.size()<<"\n";
	for(int i = 0;i<T.size();i++){
		while(pos>=0 && (T[i]!=P[pos])){
			pos = FE[pos];
		}
		pos++;
		if(pos==P.size()){
			cout<<i-P.size()+1<<"\n";
			pos = FE[pos];
		}	
	}
}

