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 s1, s2;
    cin >> s1;
    cin >> s2;
    int s1_len, s2_len;
    s1_len = s1.length();
    s2_len = s2.length();

    if(s2_len <= s1_len){
        for(int i = 0; i < s1_len; i++){
            if(s1.substr(i, s2_len) == s2){
                cout << i << "\n";
            }
    }

    }
}

