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 <string>
#include <cstdio>
using namespace std;
 
int main(){
    string a,b;
    cin >> a >> b;
    int SizeA = a.size();
    int SizeB = b.size();
    if(SizeA < SizeB) return 0;
    for (int i = 0; i < SizeA-SizeB +1 ; ++i) {
        if(a[i]== b[0]){
            if(a.substr(i,SizeB) == b) printf("%d\n",i);
        }
    }
    return 0;
}