#include<bits/stdc++.h>
#define M 131
using namespace std;
typedef unsigned long long ull;

int main(){
  string t,p;
  ull a=0,b=0,c=1;
  cin>>t>>p;
  ull tlen=t.size();
  ull plen=p.size();
  //t??¨p?????????????????°?????§??¨??£???????????????0????????????????????????????????????????¨???????
  //a??¨b???????????§????????§???a????????????????±???§???????????????????????????c??????????????´??????????????????????????????????????????????????????
  //c?????????????????????????????§?¨??????????????????????????????????
  for(int i=0;i<plen;i++)a=a*M+p[i];
  for(int i=0;i<plen;i++)b=b*M+t[i],c*=M;
  if(a==b)cout<<0<<endl;
  for(int i=plen;i<tlen;i++){
    //b??????????????§??????????????????????????????????????????????????°??????????????????????????§??????M?????????????????????????????°??????????????£?????????????????????
	b=b*M+t[i]-c*t[i-plen];
    if(a==b)printf("%d\n",i-plen+1);
  }
  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<bits/stdc++.h>
#define M 131
using namespace std;
typedef unsigned long long ull;

int main(){
  string t,p;
  ull a=0,b=0,c=1;
  cin>>t>>p;
  ull tlen=t.size();
  ull plen=p.size();
  //t??¨p?????????????????°?????§??¨??£???????????????0????????????????????????????????????????¨???????
  //a??¨b???????????§????????§???a????????????????±???§???????????????????????????c??????????????´??????????????????????????????????????????????????????
  //c?????????????????????????????§?¨??????????????????????????????????
  for(int i=0;i<plen;i++)a=a*M+p[i];
  for(int i=0;i<plen;i++)b=b*M+t[i],c*=M;
  if(a==b)cout<<0<<endl;
  for(int i=plen;i<tlen;i++){
    //b??????????????§??????????????????????????????????????????????????°??????????????????????????§??????M?????????????????????????????°??????????????£?????????????????????
	b=b*M+t[i]-c*t[i-plen];
    if(a==b)printf("%d\n",i-plen+1);
  }
  return 0;
}
```