#include<cstdio>
#include<iostream>
#include<string>

using namespace std;

typedef unsigned long long ull;

ull b=1000000007;

int main()
{
  string s, p;
  int n, m;
  ull t = 1, sh = 0, ph = 0;

  cin >> s >> p;

  n = s.length();
  m = p.length();

  if(n < m) {
    return 0;
  }

  for(int i = 0; i < m; i++) {
    t *= b;
  }
  for(int i = 0; i < m; i++) {
    sh = sh * b + s[i];
  }
  for(int i=0;i<m;i++) {
    ph = ph * b + p[i];
  }

  for(int i = 0; i + m <= n; i++) {
    if(sh == ph) {
      printf("%d\n",i);
    }
    if(i + m < n) {
      sh = sh * b + s[i + m] - s[i] * t;
    }
  }
 
  return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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<cstdio>
#include<iostream>
#include<string>

using namespace std;

typedef unsigned long long ull;

ull b=1000000007;

int main()
{
  string s, p;
  int n, m;
  ull t = 1, sh = 0, ph = 0;

  cin >> s >> p;

  n = s.length();
  m = p.length();

  if(n < m) {
    return 0;
  }

  for(int i = 0; i < m; i++) {
    t *= b;
  }
  for(int i = 0; i < m; i++) {
    sh = sh * b + s[i];
  }
  for(int i=0;i<m;i++) {
    ph = ph * b + p[i];
  }

  for(int i = 0; i + m <= n; i++) {
    if(sh == ph) {
      printf("%d\n",i);
    }
    if(i + m < n) {
      sh = sh * b + s[i + m] - s[i] * t;
    }
  }
 
  return 0;
}

```