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
#include <stdio.h>
#include <iostream>
#include <cmath>
#include <string>

int main(void) {
  std::string T;
  std::string P;

  std::cin >> T;
  std::cin >> P;
  
  if (T.size() < P.size()) {
    return 0;
  }

  int index = 0;

  for (int i = 0; i <= T.size() - P.size(); i++) {
    if (P == T.substr(i, P.size())) {
      printf("%d\n", i);
      //std::cout << i << std::endl;
    }
  }
  
  return 0;
}