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<stdio.h>
using namespace std;

int main(){

    string a, b;
    cin >> a >> b;

    int size = a.size() - b.size() + 1;
    for(int i=0; i<size; i++){
        if(b==a.substr(i, b.size())) printf("%d\n", i);
    }
    return 0;
}
