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<iomanip>
#include<algorithm>
#include<bitset>
#include<cctype>
#include<cmath>
#include<cstdio>
#include<cstring>
#include<functional>
#include<limits>
#include<list>
#include<map>
#include<set>
#include<stack>
#include<string>
#include<sstream>
#include<queue>
#include<vector>
using namespace std;

#define MOD 1000000007
#define INF 0x3f3f3f3f
#define INFL 0x3f3f3f3f3f3f3f3fLL

int main() {
	string T, P; cin >> T >> P;
	for (size_t s = T.find(P); s != string::npos; s = T.find(P, s)) {
		printf("%d\n", s++);
	}
	return 0;
}