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 REP(i,n) for(int i=0;i<n;i++)
#define FOR(i,a,b) for(int i=a;i<=b;i++)
using namespace std;

int main()
{
  string t,p; cin>>t>>p;
  int nt = t.size();
  int np = p.size();
  if(nt < np) return 0;
  REP(i,nt-np+1) if(t[i] == p[0]) if(t.substr(i,np)==p) printf("%d\n",i);
  return 0;
}