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.Arrays;
import java.util.Comparator;
import java.util.TreeSet;

public class Main {


  private static void solve() {
    int n = ni();
    int m = ni();
    int s = ni() - 1;
    int t = ni() - 1;
    int[] from = new int[m];
    int[] to = new int[m];
    int[] w1 = new int[m];
    int[] w2 = new int[m];
    for (int i = 0; i < m; i ++) {
      from[i] = ni() - 1;
      to[i] = ni() - 1;
      w1[i] = ni();
      w2[i] = ni();
    }
    int[][][] gs = packWU(n, from, to, w1);
    int[][][] gt = packWU(n, from, to, w2);
    
    long[] ds = dijk(gs, s);
    long[] dt = dijk(gt, t);
    
    long[] ret = new long[n];
    
    ret[n - 1] = dt[n - 1] + ds[n - 1];
    for (int i = n - 2; i >= 0; i --) {
      long now = dt[i] + ds[i];
      ret[i] = Math.min(ret[i + 1], now);
    }
    
    for (long v : ret) {
      System.out.println(1000000000000000L - v);
    }
  }

  public static long[] dijk(int[][][] g, int from)
  {
      int n = g.length;
      final long[] td = new long[n];
      Arrays.fill(td, Long.MAX_VALUE);
      TreeSet<Integer> q = new TreeSet<Integer>(new Comparator<Integer>(){
          public int compare(Integer a, Integer b) {
              if(td[a] - td[b] != 0)return Long.signum(td[a] - td[b]);
              return a - b;
          }
      });
      q.add(from);
      td[from] = 0;
      
      while(q.size() > 0){
          int cur = q.pollFirst();
          
          for(int i = 0;i < g[cur].length;i++){
              int next = g[cur][i][0];
              long nd = td[cur] + g[cur][i][1];
              if(nd < td[next]){
                  q.remove(next);
                  td[next] = nd;
                  q.add(next);
              }
          }
      }
      
      return td;
  }

  private static int[][][] packWU(int n, int[] from, int[] to, int[] w) {
    int sup = from.length;
    int[][][] g = new int[n][][];
    int[] p = new int[n];
    for (int i = 0; i < sup; i++)
        if (w[i] > 0)
            p[from[i]]++;
    for (int i = 0; i < sup; i++)
        if (w[i] > 0)
            p[to[i]]++;
    for (int i = 0; i < n; i++)
        g[i] = new int[p[i]][2];
    for (int i = 0; i < sup; i++) {
        if (w[i] > 0) {
            --p[from[i]];
            g[from[i]][p[from[i]]][0] = to[i];
            g[from[i]][p[from[i]]][1] = w[i];
            --p[to[i]];
            g[to[i]][p[to[i]]][0] = from[i];
            g[to[i]][p[to[i]]][1] = w[i];
        }
    }
    return g;
  }

  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}
