#include <bits/stdc++.h>
using namespace std;

typedef unsigned long long ull;
const ull B = 100000007; //???????????\?????°

//a???b???????????????????????????
bool contain(string a,string b){
  int al = a.length(), bl = b.length();
  if(al > bl) return false;
  
  //B???al???????¨????
  ull t = 1;
  for(int i=0; i< al ;i++) t *= B;
  
  //a??¨b????????????al???????????¢?????????????????\???????¨????
  ull ah = 0, bh = 0;
  for(int i=0; i<al ;i++) ah = ah * B + a[i];
  for(int i=0; i<al ;i++) bh = bh * B + b[i];
  
  //b?????´??????1???????????????????????????????????\???????????§??????
  for(int i=0; i+al<=bl; i++){
    if(ah == bh) cout<<i<<endl;
    if(i+al < bl) bh = bh * B + b[i+al] - b[i] * t;
  }
  return false;
}


int main(){
  string a,b;
  cin>>a>>b;
  contain(b,a);  
  
}
### Prompt

In cpp, your task is to solve 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 <bits/stdc++.h>
using namespace std;

typedef unsigned long long ull;
const ull B = 100000007; //???????????\?????°

//a???b???????????????????????????
bool contain(string a,string b){
  int al = a.length(), bl = b.length();
  if(al > bl) return false;
  
  //B???al???????¨????
  ull t = 1;
  for(int i=0; i< al ;i++) t *= B;
  
  //a??¨b????????????al???????????¢?????????????????\???????¨????
  ull ah = 0, bh = 0;
  for(int i=0; i<al ;i++) ah = ah * B + a[i];
  for(int i=0; i<al ;i++) bh = bh * B + b[i];
  
  //b?????´??????1???????????????????????????????????\???????????§??????
  for(int i=0; i+al<=bl; i++){
    if(ah == bh) cout<<i<<endl;
    if(i+al < bl) bh = bh * B + b[i+al] - b[i] * t;
  }
  return false;
}


int main(){
  string a,b;
  cin>>a>>b;
  contain(b,a);  
  
}
```