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

#define rep(i, N) for (int i = 0; i < (int)(N); i++)

int main() {
	string t; cin >> t;
	string s; cin >> s;
	int N = s.length();
	vector<int> a(N + 1);
	a[0] = -1;
	int k = -1;
	rep(i, N) {
		for (; k != -1 && s[k] != s[i]; k = a[k]);
		a[i + 1] = ++k;
	}
	int M = t.length();
	int i = 0, j = 0;
	while (j <= M)
		if (i < N && j < M && s[i] == t[j])
			i++, j++;
		else {
			if (i == N) printf("%d\n", j - N);
			if (i) i = a[i];
			else j++;
		}
}
### Prompt

Please formulate 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 <bits/stdc++.h>
using namespace std;

#define rep(i, N) for (int i = 0; i < (int)(N); i++)

int main() {
	string t; cin >> t;
	string s; cin >> s;
	int N = s.length();
	vector<int> a(N + 1);
	a[0] = -1;
	int k = -1;
	rep(i, N) {
		for (; k != -1 && s[k] != s[i]; k = a[k]);
		a[i + 1] = ++k;
	}
	int M = t.length();
	int i = 0, j = 0;
	while (j <= M)
		if (i < N && j < M && s[i] == t[j])
			i++, j++;
		else {
			if (i == N) printf("%d\n", j - N);
			if (i) i = a[i];
			else j++;
		}
}
```