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 <stdio.h>
#include <iostream>
#include <vector>
#include <string>
#include <math.h>
#include <algorithm>
using namespace std;
#define ull unsigned long long
const double EPS = 1e-10;

ull pow_ans(ull x, int n) {
    ull res = 1;
    while (n > 0) {
        if (n & 1) { res *= x; }
        x *= x;
        n >>= 1;
    }
    return res;
}


int main(){
  string t,p;
  cin>>t;
  cin>>p;
  ull b=1000000009;
  vector<ull> a;
  ull sum=0;
  ull ans=0;
  if(t.size()<p.size())return 0;
  for(int i=0;i<p.size();i++){
    ans+=p[i]*pow_ans(b,p.size()-1-i);
  }
  for(int i=0;i<p.size();i++){
    sum+=t[i]*pow_ans(b,p.size()-1-i);
  }
  if(ans==sum)cout<<0<<endl;
  a.push_back(sum);
  for(int i=0;i<(int)t.size()-(int)p.size();i++){
    sum-=t[i]*pow_ans(b,p.size()-1);
    sum*=b;
    sum+=t[i+p.size()];
    a.push_back(sum);
    if(ans==sum)cout<<i+1<<endl;
  }
}

