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

using namespace std;

typedef unsigned long long ull;
const ull B= 100000007;

void contain(string a, string b){
	int al=a.length();
	int bl=b.length();
	//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?????´????????????????????????????????????????????\???????????§??????
	for(int i=0;i+al<=bl;i++){
		if(ah==bh) printf("%d\n",i);
		//if(i+al<bl) 
		bh=bh*B+b[i+al]-b[i]*t;
	}
}

int main(){
	bool ans;
	string T,P;
	cin>>T;
	cin>>P;
	if(T.size()>=P.size()){
		contain(P,T); //P???T?????????????????????????
	}
}
### Prompt

Generate a Cpp solution to 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<cstdio>
#include<algorithm>
#include<string>

using namespace std;

typedef unsigned long long ull;
const ull B= 100000007;

void contain(string a, string b){
	int al=a.length();
	int bl=b.length();
	//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?????´????????????????????????????????????????????\???????????§??????
	for(int i=0;i+al<=bl;i++){
		if(ah==bh) printf("%d\n",i);
		//if(i+al<bl) 
		bh=bh*B+b[i+al]-b[i]*t;
	}
}

int main(){
	bool ans;
	string T,P;
	cin>>T;
	cin>>P;
	if(T.size()>=P.size()){
		contain(P,T); //P???T?????????????????????????
	}
}
```