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=100000007;

vector<int> contain(string a,string b){
  int al=a.size(),bl=b.size();
  vector<int> ans;
  if(al>bl)return ans;
  
  ull t=1;
  for(int i=0;i<al;i++)t*=B;

  int ah=0,bh=0;
  for(int i=0;i<al;i++)ah=ah*B+a[i];
  for(int i=0;i<al;i++)bh=bh*B+b[i];

  for(int i=0;i+al<=bl;i++){
    if(ah==bh)ans.push_back(i);
    if(i+al<bl)bh=bh*B+b[i+al]-b[i]*t;
  }
  return ans;
}

int main(){
  string t,p;
  cin>>t>>p;
  vector<int> ans=contain(p,t);
  for(int i=0;i<ans.size();i++)printf("%d\n",ans[i]);
  return 0;
}

