Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

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

Sample Output 1

999999999999998
999999999999989
999999999999979
999999999999897

After 0 years, it is optimal to do the exchange in City 1.

After 1 years, it is optimal to do the exchange in City 2.

Note that City 1 can still be visited even after the exchange office is closed.
Also note that, if it was allowed to keep 1 yen when do the exchange in City 2 and change the remaining yen into snuuk, we could reach City 3 with 999999999999998 snuuk, but this is NOT allowed.

After 2 years, it is optimal to do the exchange in City 3.

After 3 years, it is optimal to do the exchange in City 4.
Note that the same train can be used multiple times.

Sample Input 2

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

Sample Output 2

999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994

Solution in C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

public class Node
{
    public long Yen;
    public long Snuke;
    public List<Train> Trains = new List<Train>();

    public void Excange()
    {
        Snuke = Math.Max(Yen, Snuke);
    }
}

public class Train
{
    public int Dest;
    public long Yen;
    public long Snuke;

    public Train(int dest, int yen, int snuke)
    {
        Dest = dest;
        Yen = yen;
        Snuke = snuke;
    }
}

class Solution
{
    const long MaxYen = 1000000000000000;

    static void Solve(Node[] nodes, int start, int goal, int year)
    {
        var visited = new bool[nodes.Length];
        nodes[start].Yen = MaxYen;
        if (start > year)
        {
            nodes[start].Snuke = MaxYen;
        }

        var currents = new HashSet<int>(Enumerable.Range(0, nodes.Length).Where(i => nodes[i].Yen > 0));
        while (currents.Count > 0)
        {
            var nexts = new HashSet<int>();

            foreach (var cur in currents)
            {
                var curNode = nodes[cur];
                if (cur > year && curNode.Yen > 0)
                {
                    curNode.Excange();
                }

                foreach (var train in nodes[cur].Trains)
                {
                    bool add = false;
                    var nextNode = nodes[train.Dest];
                    var yen = curNode.Yen - train.Yen;
                    if (nextNode.Yen < yen)
                    {
                        add = true;
                        nextNode.Yen = yen;
                    }

                    var snuke = curNode.Snuke - train.Snuke;
                    if (nextNode.Snuke < snuke)
                    {
                        add = true;
                        nextNode.Snuke = snuke;
                    }

                    if (add)
                    {
                        nexts.Add(train.Dest);
                    }
                }
            }

            currents = nexts;
        }
    }

    static void Main()
    {
        var vals = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        int n = vals[0];
        int m = vals[1];
        int start = vals[2];
        int goal = vals[3];

        var nodes = Enumerable.Range(0, n + 1).Select(_ => new Node()).ToArray();
        for (int i = 0; i < m; i++)
        {
            vals = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            var u = vals[0];
            var v = vals[1];
            var yen = vals[2];
            var snuke = vals[3];
            nodes[u].Trains.Add(new Train(v, yen, snuke));
            nodes[v].Trains.Add(new Train(u, yen, snuke));
        }

        var answer = new StringBuilder();
        for (int year = 0; year < n; year++)
        {
            for (int i = 0; i < nodes.Length; i++)
            {
                nodes[i].Snuke = 0;
            }

            Solve(nodes, start, goal, year);
            var max = nodes[goal].Snuke;
            answer.AppendLine(max.ToString());
        }

        Console.WriteLine(answer);
    }
}