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()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    string t, p;
    cin>>t>>p;
    for(int pos=0; pos<t.length(); pos++) {
        pos = t.find(p, pos);
        if(pos==string::npos) break;
        cout<<pos<<'\n';
    }
    return 0;
}