#include <iostream>
#include <cstring>
using namespace std;

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    char t[1000001], p[10001];
    int jt[10001];
    cin.getline(t, 1000001);
    int tl=cin.gcount()-1;
    cin.getline(p, 10001);
    int pl=cin.gcount()-1;
    if(pl>tl) return 0;

    jt[0]=-1;
    jt[1]=0;
    int i=2, j=0;
    while(i<=pl){
        if(p[i-1]==p[j]){
            jt[i]=j+1;
            ++i;
            ++j;
        } else if(j>0) j=jt[j];
        else jt[i++]=0;
    }
    i=j=0;
    while(i<tl){
        if(t[i]==p[j]){
            ++i;
            ++j;
            if(j==pl){
                cout<<i-pl<<'\n';
                j=jt[j];
            }
        }else if(j==0) ++i;
        else j=jt[j];
    }
    return 0;
}
### Prompt

Please provide a Cpp coded solution to the problem described below:

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 <cstring>
using namespace std;

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    char t[1000001], p[10001];
    int jt[10001];
    cin.getline(t, 1000001);
    int tl=cin.gcount()-1;
    cin.getline(p, 10001);
    int pl=cin.gcount()-1;
    if(pl>tl) return 0;

    jt[0]=-1;
    jt[1]=0;
    int i=2, j=0;
    while(i<=pl){
        if(p[i-1]==p[j]){
            jt[i]=j+1;
            ++i;
            ++j;
        } else if(j>0) j=jt[j];
        else jt[i++]=0;
    }
    i=j=0;
    while(i<tl){
        if(t[i]==p[j]){
            ++i;
            ++j;
            if(j==pl){
                cout<<i-pl<<'\n';
                j=jt[j];
            }
        }else if(j==0) ++i;
        else j=jt[j];
    }
    return 0;
}
```