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;

void buildFail(const string& t, vector<int>& fail) {
    int m = t.size();
    fail.resize(m + 1);
    int j = -1;
    fail[0] = -1;
    for(int i = 1; i <= m; ++i) {
        while(j >= 0 && t[j] != t[i - 1]) j = fail[j];
        fail[i] = ++j;
    }
}

void match(const string& s, const string& t, vector<int>& res) {
    vector<int> fail;
    buildFail(t, fail);
    int n = s.size(), m = t.size();
    for(int i = 0, k = 0; i < n; ++i) {
        while(k >= 0 && t[k] != s[i]) k = fail[k];
        ++k;
        if(k >= m) {
            res.emplace_back(i - m + 1);
            k = fail[k];
        }
    }
}
int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    string s, t;
    cin >> s >> t;
    vector<int> res;
    match(s, t, res);
    for(int x : res)
        cout << x << '\n';
    return 0;
}