#include <iostream>
#include <vector>
using namespace std;

int main() {
  cin.tie(0);
  ios_base::sync_with_stdio(false);
  string t, p;
  cin >> t >> p;
  // `pi[i]`: the length of the longest prefix of `p` that is a suffix
  // of p[1..i]
  vector<int> pi(p.size() + 1);
  pi[0] = -1;
  for (int i = 1, k = -1; i <= p.size(); ++i) {
    while (k >= 0 && p[i - 1] != p[k])
      k = pi[k];
    pi[i] = ++k; // either k=-1, so we want pi[i]=0, or we matched p[k] to
                 // p[i-1], so we want pi[i]=k+1
  }

  int j = 0;                           // number of matched characters
  for (int i = 0; i < t.size(); ++i) { // position in text
    while (j >= 0 && t[i] != p[j])
      j = pi[j];
    ++j; // either j=-1, so we want to record that we've matched 0 characters,
         // or we just matched the j+1th character of p with t[i], so we want to
         // increment j
    if (j == p.size()) {
      printf("%d\n", i - p.size() + 1);
      j = pi[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 <iostream>
#include <vector>
using namespace std;

int main() {
  cin.tie(0);
  ios_base::sync_with_stdio(false);
  string t, p;
  cin >> t >> p;
  // `pi[i]`: the length of the longest prefix of `p` that is a suffix
  // of p[1..i]
  vector<int> pi(p.size() + 1);
  pi[0] = -1;
  for (int i = 1, k = -1; i <= p.size(); ++i) {
    while (k >= 0 && p[i - 1] != p[k])
      k = pi[k];
    pi[i] = ++k; // either k=-1, so we want pi[i]=0, or we matched p[k] to
                 // p[i-1], so we want pi[i]=k+1
  }

  int j = 0;                           // number of matched characters
  for (int i = 0; i < t.size(); ++i) { // position in text
    while (j >= 0 && t[i] != p[j])
      j = pi[j];
    ++j; // either j=-1, so we want to record that we've matched 0 characters,
         // or we just matched the j+1th character of p with t[i], so we want to
         // increment j
    if (j == p.size()) {
      printf("%d\n", i - p.size() + 1);
      j = pi[j];
    }
  }
}

```