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>
using namespace std;
char A[1000005],B[10005];
int Next[10001];
void getNext(int lb){
	int j=0, k=-1;
	Next[0] = -1;
	while(j < lb)
		if(k==-1 || B[k]==B[j])
			Next[++j] = ++k;
		else k = Next[k];
}
void Find(int la, int lb){
	int i=0, j=0;
	while(i<la)
		if(j==-1 || A[i]==B[j]){
			i++, j++;
			if(j == lb){
				cout << i - j << endl;
				j = Next[j];
			}
		}
		else 
			j = Next[j];
}
int main()
{	
	scanf("%s%s",A,B);
	int la=strlen(A), lb=strlen(B);
	getNext(lb);
	Find(la, lb);
	return 0;
}

