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>
#define optimizar_io ios_base::sync_with_stdio(0);cin.tie
using namespace std;

int FE[100002];

void FuncionError(string &t){	
	FE[0] = -1;
	for(int i = 0; i < t.size();){
		int pos = FE[i];
		while(pos >= 0 && t[pos] != t[i])
			pos = FE[pos];
		FE[++i] = ++pos;
	}
}

void Aparece(string &s, string &t){
	int pos = 0;
	for(int i = 0; i < s.size(); i++){
		while(pos >= 0 && s[i] != t[pos] )
			pos = FE[pos];
		pos++;
		if(pos == t.size()){
			cout << i - t.size() + 1 << '\n';
			pos = FE[pos];
		}
	}
}

int main(){

	string s,t;


	optimizar_io(0);

	cin >> s >> t;

	FuncionError(t);
	Aparece(s,t);

	return 0;
}
