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 N 950527
using namespace std;
typedef unsigned long long ull;
int main(){
  string s,p;
  cin>>s>>p;
  ull a=0,b=0,g=1;
  for(int i=0;i<p.size();i++)b*=N,b+=s[i],g*=N;
  for(int i=0;i<p.size();i++)a*=N,a+=p[i];
  if(b==a)printf("0\n");

  for(int i=p.size();i<(int)s.size();i++){
    b*=N,b+=s[i],b-=s[i-p.size()]*g; 
    if(b==a)printf("%d\n",i-p.size()+1);
  }
  return 0;
}