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>

using namespace std;

int main(){
    string S, T;
    cin >> S >> T;

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