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
#define _USE_MATH_DEFINES
#include <algorithm>
#include <cstdio>
#include <functional>
#include <iostream>
#include <cfloat>
#include <climits>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <time.h>
#include <vector>
#include <random>
#include <list>
using namespace std;
 
typedef long double ld;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> i_i;
typedef pair<ll, int> ll_i;
typedef pair<int, ll> i_ll;
typedef pair<double, int> d_i;
typedef pair<ll, ll> ll_ll;
typedef pair<double, double> d_d;
struct edge { int u, v; ll w; };
 
#define rep(i, N) for (int i = 0; i < (int)(N); i++)
#define pb push_back
 
int INF = INT_MAX / 10;
ll MOD = 1000000007;
ll _MOD = 1000000009;
double EPS = 1e-10;

int main() {
	string t; cin >> t;
	string s; cin >> s;
	int N = s.length();
	vector<int> a(N + 1);
	a[0] = -1;
	int k = -1;
	rep(i, N) {
		for (; k != -1 && s[k] != s[i]; k = a[k]);
		a[i + 1] = ++k;
	}
	int M = t.length();
	int i = 0, j = 0;
	while (j <= M)
		if (i < N && j < M && s[i] == t[j])
			i++, j++;
		else {
			if (i == N) printf("%d\n", j - N);
			if (i) i = a[i];
			else j++;
		}
}