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>

#define rep(i,n) for(int i=0;i<n;++i)
using namespace std;

typedef unsigned long long ull;
const ull b=10007;

string t,p;

int main(void){
	cin >> t >> p;
	int n=t.size(),m=p.size();
	ull ph=0;
	rep(i,m) ph=ph*b+p[i];
	ull th=0;
	rep(i,m) th=th*b+t[i];
	ull fix=1;
	rep(i,m) fix*=b;

	for(int i=0;i+m<=n;++i){
		if(ph==th) cout << i << endl;
		th=th*b-fix*t[i]+t[i+m];
	}
	return 0;
}