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

using ull = unsigned __int128;

vector<int> res;

void Rolling_Hash(const string& a, const string& b) {
	const ull B = 100000007;
	int al = a.length(), bl = b.length();
	if (al > bl) return;

	ull t = 1, ah = 0, bh = 0;
	for (int i = 0; i < al; i++) t *= B;
	for (int i = 0; i < al; i++) ah = ah * B + a[i];
	for (int i = 0; i < al; i++) bh = bh * B + b[i];
	for (int i = 0; i + al <= bl; i++) {
		if (ah == bh) {
			res.push_back(i);
		}
		if (i + al < bl) bh = bh * B + b[i + al] - b[i] * t;
	}
}

int main()
{
	string T, P;
	cin.sync_with_stdio(false);
	cin >> T >> P;
	Rolling_Hash(P, T);
	for (auto &i : res) {
		cout << i << endl;
	}
	return 0;
}
### Prompt

Construct a cpp code solution to the problem outlined:

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;

using ull = unsigned __int128;

vector<int> res;

void Rolling_Hash(const string& a, const string& b) {
	const ull B = 100000007;
	int al = a.length(), bl = b.length();
	if (al > bl) return;

	ull t = 1, ah = 0, bh = 0;
	for (int i = 0; i < al; i++) t *= B;
	for (int i = 0; i < al; i++) ah = ah * B + a[i];
	for (int i = 0; i < al; i++) bh = bh * B + b[i];
	for (int i = 0; i + al <= bl; i++) {
		if (ah == bh) {
			res.push_back(i);
		}
		if (i + al < bl) bh = bh * B + b[i + al] - b[i] * t;
	}
}

int main()
{
	string T, P;
	cin.sync_with_stdio(false);
	cin >> T >> P;
	Rolling_Hash(P, T);
	for (auto &i : res) {
		cout << i << endl;
	}
	return 0;
}
```