Kenkoooo is planning a trip in Republic of Snuke. In this country, there are n cities and m trains running. The cities are numbered 1 through n, and the i-th train connects City u_i and v_i bidirectionally. Any city can be reached from any city by changing trains.

Two currencies are used in the country: yen and snuuk. Any train fare can be paid by both yen and snuuk. The fare of the i-th train is a_i yen if paid in yen, and b_i snuuk if paid in snuuk.

In a city with a money exchange office, you can change 1 yen into 1 snuuk. However, when you do a money exchange, you have to change all your yen into snuuk. That is, if Kenkoooo does a money exchange when he has X yen, he will then have X snuuk. Currently, there is a money exchange office in every city, but the office in City i will shut down in i years and can never be used in and after that year.

Kenkoooo is planning to depart City s with 10^{15} yen in his pocket and head for City t, and change his yen into snuuk in some city while traveling. It is acceptable to do the exchange in City s or City t.

Kenkoooo would like to have as much snuuk as possible when he reaches City t by making the optimal choices for the route to travel and the city to do the exchange. For each i=0,...,n-1, find the maximum amount of snuuk that Kenkoooo has when he reaches City t if he goes on a trip from City s to City t after i years. You can assume that the trip finishes within the year.

Constraints

* 2 \leq n \leq 10^5
* 1 \leq m \leq 10^5
* 1 \leq s,t \leq n
* s \neq t
* 1 \leq u_i < v_i \leq n
* 1 \leq a_i,b_i \leq 10^9
* If i\neq j, then u_i \neq u_j  or v_i \neq v_j.
* Any city can be reached from any city by changing trains.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


n m s t
u_1 v_1 a_1 b_1
:
u_m v_m a_m b_m


Output

Print n lines. In the i-th line, print the maximum amount of snuuk that Kenkoooo has when he reaches City t if he goes on a trip from City s to City t after i-1 years.

Examples

Input

4 3 2 3
1 4 1 100
1 2 1 10
1 3 20 1


Output

999999999999998
999999999999989
999999999999979
999999999999897


Input

8 12 3 8
2 8 685087149 857180777
6 7 298270585 209942236
2 4 346080035 234079976
2 5 131857300 22507157
4 8 30723332 173476334
2 6 480845267 448565596
1 4 181424400 548830121
4 5 57429995 195056405
7 8 160277628 479932440
1 6 475692952 203530153
3 5 336869679 160714712
2 7 389775999 199123879


Output

999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
import java.util.*;
import java.io.*;
import java.math.*;
 
 
import static java.lang.Math.*;
import static java.util.Arrays.*;
import static java.util.Collections.*;
 
public class Main{
    static final long mod=1000000007;
    
    public  static void main(String[] args)   throws Exception, IOException{
        Reader sc = new Reader(System.in);
        PrintWriter out=new PrintWriter(System.out);
        // int n=sc.nextInt();
        // char c[][] = new char[h][w];
        // char c[]=sc.nextString().toCharArray();
        // for(int i=0; i<n; i++) {a[i]=sc.nextInt();}
        int n=sc.nextInt();
        int m=sc.nextInt();
        int start = sc.nextInt() - 1, goal = sc.nextInt() - 1;

        long d[] = new long[n];
        long g[] = new long[n];
        fill(d, 1L<<62);
        fill(g, 1L<<62);
        d[start] = 0;
        g[goal] = 0;
        
        ArrayList<Long> lise[] = new ArrayList[n];
        ArrayList<Long> liss[] = new ArrayList[n];
        long sf=1L<<20;
        for (int i=0; i<n; i++)lise[i] =  new ArrayList<Long>();
        for (int i=0; i<n; i++)liss[i] =  new ArrayList<Long>();
        for (int i=0; i<m; i++) {
            int a=sc.nextInt()-1,
                b=sc.nextInt()-1;
              long  q=sc.nextLong(),
                    w=sc.nextLong();
                lise[a].add( q*sf + b);
                lise[b].add( q*sf + a);
                liss[a].add( w*sf + b);
                liss[b].add( w*sf + a);
        }

        PriorityQueue<P> que = new PriorityQueue<P>();
        que.add(new P(start, d[start]));

        while(!que.isEmpty()) {
            P p = que.poll();   
            int cr = p.id;
            // db(cr);
            if(d[cr] < p.d) continue;
            long or, es; int to;
            for( int t=0; t<lise[cr].size(); t++ ){
                or = lise[cr].get(t);
                to = (int)( or & (sf-1));
                es = or>>20;
                if( d[to] > d[cr] + es) {
                    d[to] = d[cr] + es;
                    que.add(new P(to, d[to]));
                }
            }
        }
        // db(d);

        que.clear();
        que.add(new P(goal, g[goal]));
        while(!que.isEmpty()) {
            P p = que.poll();
            int cr = p.id;
            // db(cr);
            if(g[cr] < p.d) continue;
            long or, es; int to;
            for( int t=0; t<liss[cr].size(); t++ ){
                or = liss[cr].get(t);
                to = (int)( or & (sf-1));
                es = or>>20;
                // db(to,es);
                if( g[to] > g[cr] + es) {
                    g[to] = g[cr] + es;
                    que.add(new P(to, g[to]));
                }
            }
        }
        P p[] = new P[n];
        for( int t=0; t<n; t++ ){
            p[t] = new P(t, d[t]+g[t] );
        }
        sort(p);
        long M=1000000000000000L;
        int x=0;

        for( int t=0; t<n; t++ ){
            while(p[x].id<=t-1)x++;
            out.println(M - p[x].d);
        }

        // out.println();
        out.flush();
    }
    

    static void db(Object... os){
        System.err.println(Arrays.deepToString(os));
    }
     
    static boolean validpos(int x,int y,int r, int c){
        return x<r && 0<=x && y<c && 0<=y;
    }
    
    static boolean bit(long x,int k){
        // weather k-th bit (from right) be one or zero
        return  ( 0 < ( (x>>k) & 1 )  )  ? true:false;
    }    
}

class P implements Comparable<P>{
        long d;
        int id;
        P(int  id, long d) {
            this.id=id;
            this.d=d;
        } 
          
        public int compareTo(P p){
            long r = d - p.d;
            if(r==0)return 0;
            else return r > 0 ? 1 : -1;//des
        }
    }

class Reader
{ 
    private BufferedReader x;
    private StringTokenizer st;
    
    public Reader(InputStream in)
    {
        x = new BufferedReader(new InputStreamReader(in));
        st = null;
    }
    public String nextString() throws IOException
    {
        while( st==null || !st.hasMoreTokens() )
            st = new StringTokenizer(x.readLine());
        return st.nextToken();
    }
    public int nextInt() throws IOException
    {
        return Integer.parseInt(nextString());
    }
    public long nextLong() throws IOException
    {
        return Long.parseLong(nextString());
    }
    public double nextDouble() throws IOException
    {
        return Double.parseDouble(nextString());
    }
}