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 <iostream>
#include<bits/stdc++.h>
using namespace std;
vector<int> table,res;
string s,t;
vector<int> pre_kmp(string s){
    vector<int> v(s.size()+1);
    int k;
    v[0]=-1;
    for(int i=1;i<=s.size();i++){
        k=v[i-1];
        while(k>=0){
            if(s[k]==s[i-1])break;
            else k=v[k];
        }
        v[i]=k+1;
    }
    return v;
}
void match(string s, string t){
    int head = 0, j = 0, slen=s.size(),tlen=t.size();
    while(head + j < slen){
        if(t[j] == s[head + j]){
            if(++j != tlen) continue;
            res.push_back(head);
        }
        head += j - table[j], j = max(table[j], 0);
    }
}
int main(void){
    cin>>s>>t;
    table=pre_kmp(t);
    match(s,t);
    for(auto x:res)cout<<x<<endl;
}

