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;

int main(){
	string a;
	string b;
	long long int i;
	
	cin>>a>>b; //getchar();
	if(a.length()>=b.length()){
		for(i=0; i<=(a.length() - b.length()); i++){
			if(a.substr(i,b.length())==b){
			    printf("%lld\n",i);
			} 
		}
	}

	//getchar();
	return 0;
}
