#include<iostream>
#include<string>
#include<algorithm>
#include<vector>
using namespace std;
typedef unsigned long long int ull;

const ull B=1e9+7;//base of hash

bool contain(string s,string a)
{
	int sl=s.length(),al=a.length();
	if(sl<al)return false;
	
	ull t=1;
	for(int i=0;i<al;i++)t*=B;
	
	ull sh=0,ah=0;
	for(int i=0;i<al;i++)
	{
		sh=sh*B+s[i];
		ah=ah*B+a[i];
	}
	
	if(sh==ah)return true;
	
	for(int i=0;i+al<sl;i++)
	{
		sh=sh*B+s[i+al]-s[i]*t;
		if(sh==ah)return true;
	}
	
	return false;
}

vector<int> match(string s,string a)
{
	int sl=s.length(),al=a.length();
	vector<int> ans;
	if(sl<al)return ans;
	ull t=1;
	ull ah=0,sh=0;
	for(int i=0;i<al;i++)
	{
		sh=sh*B+s[i];
		ah=ah*B+a[i];
		t*=B;
	}
	
	if(sh==ah)ans.push_back(0);
	
	for(int i=0;i+al<sl;i++)
	{
		sh=sh*B+s[i+al]-s[i]*t;
		if(sh==ah)ans.push_back(i+1);
	}
	return ans;
}

int main()
{
	string s,a;
	cin>>s>>a;
	vector<int> m=match(s,a);
	for(int i=0;i<m.size();i++)
	{
		cout<<m[i]<<endl;
	}
	return 0;
}
### Prompt

Please create a solution in cpp 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<string>
#include<algorithm>
#include<vector>
using namespace std;
typedef unsigned long long int ull;

const ull B=1e9+7;//base of hash

bool contain(string s,string a)
{
	int sl=s.length(),al=a.length();
	if(sl<al)return false;
	
	ull t=1;
	for(int i=0;i<al;i++)t*=B;
	
	ull sh=0,ah=0;
	for(int i=0;i<al;i++)
	{
		sh=sh*B+s[i];
		ah=ah*B+a[i];
	}
	
	if(sh==ah)return true;
	
	for(int i=0;i+al<sl;i++)
	{
		sh=sh*B+s[i+al]-s[i]*t;
		if(sh==ah)return true;
	}
	
	return false;
}

vector<int> match(string s,string a)
{
	int sl=s.length(),al=a.length();
	vector<int> ans;
	if(sl<al)return ans;
	ull t=1;
	ull ah=0,sh=0;
	for(int i=0;i<al;i++)
	{
		sh=sh*B+s[i];
		ah=ah*B+a[i];
		t*=B;
	}
	
	if(sh==ah)ans.push_back(0);
	
	for(int i=0;i+al<sl;i++)
	{
		sh=sh*B+s[i+al]-s[i]*t;
		if(sh==ah)ans.push_back(i+1);
	}
	return ans;
}

int main()
{
	string s,a;
	cin>>s>>a;
	vector<int> m=match(s,a);
	for(int i=0;i<m.size();i++)
	{
		cout<<m[i]<<endl;
	}
	return 0;
}
```