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.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.PriorityQueue;
import java.util.Scanner;

public class Main {
  static Scanner sc = new Scanner(System.in);
  static ArrayList<ArrayList<Edge>> g = new ArrayList<>();
  static int N, M, S, T;

  public static void main(String[] args) {
    N = sc.nextInt();
    M = sc.nextInt();
    S = sc.nextInt() - 1;
    T = sc.nextInt() - 1;
    for (int i = 0; i < N; i++) {
      g.add(new ArrayList<>());
    }
    for (int i = 0; i < M; i++) {
      int U = Integer.parseInt(sc.next()) - 1;
      int V = Integer.parseInt(sc.next()) - 1;
      int A = Integer.parseInt(sc.next());
      int B = Integer.parseInt(sc.next());
      g.get(U).add(new Edge(V, A, B));
      g.get(V).add(new Edge(U, A, B));
    }
    long[] sd = shortest(S);
    long[] td = shortest(T);
    long[] ans = new long[N];
    ans[N - 1] = sd[N - 1] + td[N - 1];
    for (int i = N - 2; i >= 0; i--) {
      ans[i] = Math.min(ans[i + 1], sd[i] + td[i]);
    }
    PrintWriter writer = new PrintWriter(System.out);
    for (int i = 0; i < N; i++) {
      writer.println(1_000_000_000_000_000L - ans[i]);
    }
    writer.flush();
  }

  static long[] shortest(int from) {
    final long INF = (long) 1e17;
    long[] dist = new long[N];
    Arrays.fill(dist, INF);
    boolean[] visited = new boolean[N];
    PriorityQueue<State> q = new PriorityQueue<>();
    q.add(new State(0, from));
    while (!q.isEmpty()) {
      State s = q.poll();
      if (visited[s.p]) continue;
      dist[s.p] = s.d;
      visited[s.p] = true;
      for (Edge e : g.get(s.p)) {
        if (visited[e.to]) continue;
        long nd = s.d + (from == S ? e.a : e.b);
        if (dist[e.to] <= nd) continue;
        dist[e.to] = nd;
        q.add(new State(nd,e.to));
      }
    }
    return dist;
  }

  static class State implements Comparable<State> {
    long d;
    int p;

    public State(long d, int p) {
      this.d = d;
      this.p = p;
    }

    @Override
    public int compareTo(State o) {
      return Long.compare(this.d, o.d);
    }
  }

  static class Edge {
    int to;
    long a, b;

    public Edge(int to, int a, int b) {
      this.to = to;
      this.a = a;
      this.b = b;
    }
  }
}
