#include <iostream>
#include <string>
#include <cstdio>

using namespace std;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    
    string T, P;
    int Tlen, Plen;

    cin >> T >> P;
    Tlen = T.size();
    Plen = P.size();

    for (int i = 0; i <= Tlen - Plen; i++) {
        if (T[i] == P[0]) {
            if (P == T.substr(i, Plen)) {
                cout << i << "\n";
            }
        }
    }
    
    return 0;
}
### Prompt

Create a solution in CPP for the following problem:

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

### Response

```cpp
#include <iostream>
#include <string>
#include <cstdio>

using namespace std;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    
    string T, P;
    int Tlen, Plen;

    cin >> T >> P;
    Tlen = T.size();
    Plen = P.size();

    for (int i = 0; i <= Tlen - Plen; i++) {
        if (T[i] == P[0]) {
            if (P == T.substr(i, Plen)) {
                cout << i << "\n";
            }
        }
    }
    
    return 0;
}
```