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>
#define base 950527
using namespace std;
typedef unsigned long long ll;
map <ll,ll> map;

int main(){
  string a,b;
  cin>>a>>b;
  
  ll hs=0,n=0,t=1;
  for(int i=0;i<b.size();i++){
    hs=hs*base+b[i];
    n=n*base+a[i];
    t*=base;
  }
  
  if(hs==n) cout <<0<<endl;
  for(int i=b.size();i<a.size();i++){
    n=n*base-t*a[i-b.size()];
    n+=a[i];
    if(hs==n) cout <<i-b.size()+1<<endl;
  }
  return 0;
}