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
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
#define rep(i,n) for(int i=0;i<n;i++)
#define cinf(n,x) for(int i=0;i<(n);i++)cin>>x[i];
#define ft first
#define sc second
#define pb push_back
#define lb lower_bound
#define ub upper_bound
#define all(v) (v).begin(),(v).end()
#define mod 1000000007
#define FS fixed<<setprecision(15)
using namespace std;
typedef long long ll;
template<class T> using V=vector<T>;
using Graph = vector<vector<int>>;
using P=pair<ll,ll>;
typedef unsigned long long ull;
typedef long double ldouble;
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }

const ll INF=1e18;

const ull B=1000000007;//ハッシュの基数

//aはbに含まれているか？
void contain(string a,string b){
    int al=a.length(),bl=b.length();
    if(al>bl) return;

    //Bのal乗を計算
    ull t=1;
    for(int i=0;i<al;i++) t*=B;

    //aとbの最初のal文字に関するハッシュ値を計算
    ull ah=0,bh=0;
    for(int i=0;i<al;i++) ah=ah*B+a[i];
    for(int i=0;i<al;i++) bh=bh*B+b[i];

    //bの場所を1つずつ進めながらハッシュ値をチェック
    for(int i=0;i+al<=bl;i++){
        if(ah==bh) cout<<i<<'\n';//bのi文字目からのal文字が一致
        if(i+al<bl) bh=bh*B+b[i+al]-b[i]*t;
    }
}

int main(){
    string t,p;
    cin>>t>>p;
    contain(p,t);
}
