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 <string.h>

int main(){

  char I[1000001], L[10001];
  int i, j, in, ln, state;

  scanf("%s", I);
  scanf("%s", L);

  in=strlen(I);
  ln=strlen(L);

  for(i=0 ;i<in; i++)
    if(strncmp(&I[i], L, ln)==0)printf("%d\n",i);

  return 0;

}