#include "bits/stdc++.h"
#define LF '\n'
#define ALL(x) x.begin(), x.end()
#define iostreamBooster() { cin.tie(nullptr); ios_base::sync_with_stdio(false); }
using namespace std;
typedef int64_t i64;
typedef pair<int,int> pii;
template<class A, class B>inline bool chmax(A &a, const B &b){return b>a ? a=b,1 : 0;}
template<class A, class B>inline bool chmin(A &a, const B &b){return b<a ? a=b,1 : 0;}
constexpr int INF = 0x3f3f3f3f;
template<class Itr> void dump(Itr begin, Itr end) { for (;begin != end; ++begin) clog << *begin << LF; }

signed main()
{
  string t, p;
  cin >> t >> p;

  const int len = (int)t.length();
  int begin = 0;

  for (;;) {

    const int found = t.find(p, begin);

    if (found != string::npos) {
      cout << found << LF;
      begin = found + 1;
    } else {
      break;
    }
  }

  return 0;
}



### 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"
#define LF '\n'
#define ALL(x) x.begin(), x.end()
#define iostreamBooster() { cin.tie(nullptr); ios_base::sync_with_stdio(false); }
using namespace std;
typedef int64_t i64;
typedef pair<int,int> pii;
template<class A, class B>inline bool chmax(A &a, const B &b){return b>a ? a=b,1 : 0;}
template<class A, class B>inline bool chmin(A &a, const B &b){return b<a ? a=b,1 : 0;}
constexpr int INF = 0x3f3f3f3f;
template<class Itr> void dump(Itr begin, Itr end) { for (;begin != end; ++begin) clog << *begin << LF; }

signed main()
{
  string t, p;
  cin >> t >> p;

  const int len = (int)t.length();
  int begin = 0;

  for (;;) {

    const int found = t.find(p, begin);

    if (found != string::npos) {
      cout << found << LF;
      begin = found + 1;
    } else {
      break;
    }
  }

  return 0;
}



```