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<bits/stdc++.h>
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;
}