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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Runtime.CompilerServices;
using System.Text;
using static Template;
using static System.Console;
using static System.Convert;
using static System.Math;
using Pi = Pair<int, int>;
using Graph;
//using DataStructure;

class Solver
{
    public void Solve()
    {
        int num, m, s, t;
        Input.Make(out num, out m, out s, out t); s--; t--;
        var kg = new Dijkstra(num);
        var yg = new Dijkstra(num);
        for (var i = 0; i < m; i++)
        {
            int a, b, y, k;
            Input.Make(out a, out b, out y, out k);
            a--; b--;
            kg.AddEdge(a, b, k);
            kg.AddEdge(b, a, k);
            yg.AddEdge(a, b, y);
            yg.AddEdge(b, a, y);
        }
        var kdist = kg.Calc(t);
        var ydist = yg.Calc(s);
        var inf = (long)1e15;
        var res = new long[num]; var min = 0L;
        for (var i = num - 1; i >= 0; i--)
        {
            chmax(ref min, inf - kdist[i] - ydist[i]);
            res[i] = min;
        }
        WriteLine(string.Join("\n", res));
    }
}
namespace Graph
{
    #region テンプレート
    public class Graph<E> where E : Edge
    {
        public List<E>[] Edges { get; set; }
        public int Count { get; }
        public Graph(int count)
        {
            Count = count;
            Edges = Create(count, () => new List<E>());
        }
    }
    public class Directed<E> : Graph<E> where E : Edge
    { public Directed(int count) : base(count) { } }
    public class Undirected<E> : Graph<E> where E : Edge
    { public Undirected(int count) : base(count) { } }

    public interface IWeight<T> where T : IComparable<T> { T Weight { get; set; } }
    public interface INNegWeight<T> : IWeight<T> where T : IComparable<T> { }
    public interface IEdge
    {
        int From { get; }
        int To { get; }
    }
    public class Edge
    {
        public int From { get; set; }
        public int To { get; set; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public Edge(int from, int to)
        { From = from; To = to; }
    }
    #endregion
}
namespace Graph
{
    using Number = System.Int32;
    public class Dijkstra
    {
        private Graph<DijEdge> g;
        public Dijkstra(int c) { g = new Graph<DijEdge>(c); }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void AddEdge(int from, int to, Number weight)
         => g.Edges[from].Add(new DijEdge(from, to, weight));
        public Number[] Calc(int st = 0)
        {
            var pq = new PriorityQueue<Pair<Number, int>>(false);
            pq.Enqueue(new Pair<Number, int>(0, st));
            var dist = Create(g.Count, () => Number.MaxValue);
            dist[st] = 0;
            var use = new bool[g.Count];
            while (pq.Count != 0)
            {
                var p = pq.Dequeue();
                if (p.v1 > dist[p.v2] || use[p.v2]) continue;
                use[p.v2] = true;
                foreach (var e in g.Edges[p.v2])
                    if (!use[e.To] && chmin(ref dist[e.To], p.v1 + e.Weight))
                        pq.Enqueue(new Pair<Number, int>(dist[e.To], e.To));
            }
            return dist;
        }

        public class DijEdge : Edge, INNegWeight<Number>
        {
            public Number Weight { get; set; }
            [MethodImpl(MethodImplOptions.AggressiveInlining)]
            public DijEdge(int from, int to, Number weight) : base(from, to)
            { Weight = weight; }
        }
    }
}

public class PriorityQueue<T> where T : IComparable<T>
{
    public List<T> _item;
    public int Count { get { return _item.Count; } }
    public bool IsMaxHeap { get; set; }
    public T Peek { get { return _item[0]; } }
    public PriorityQueue(bool IsMaxHeap = true, IEnumerable<T> list = null)
    {
        _item = new List<T>();
        this.IsMaxHeap = IsMaxHeap;
        if (list != null)
        {
            _item.AddRange(list);
            Build();
        }
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    private int Compare(int i, int j) => (IsMaxHeap ? 1 : -1) * _item[i].CompareTo(_item[j]);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    private void Swap(int i, int j) { var t = _item[i]; _item[i] = _item[j]; _item[j] = t; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    private int Parent(int i)
        => (i - 1) >> 1;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    private int Left(int i)
        => (i << 1) + 1;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public T Enqueue(T val)
    {
        int i = _item.Count;
        _item.Add(val);
        while (i > 0)
        {
            int p = Parent(i);
            if (Compare(i, p) > 0)
                Swap(i, p);
            i = p;
        }
        return val;
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    private void Heapify(int index)
    {
        for (int i = index, j; (j = Left(i)) < _item.Count; i = j)
        {
            if (j != _item.Count - 1 && Compare(j, j + 1) < 0) j++;
            if (Compare(i, j) < 0)
                Swap(i, j);
        }
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public T Dequeue()
    {
        T val = _item[0];
        _item[0] = _item[_item.Count - 1];
        _item.RemoveAt(_item.Count - 1);
        Heapify(0);
        return val;
    }
    private void Build()
    {
        for (var i = (_item.Count >> 1) - 1; i >= 0; i--)
            Heapify(i);
    }
}
public class Template
{
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmin<T>(ref T num, T val) where T : IComparable<T>
    { if (num.CompareTo(val) == 1) { num = val; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmax<T>(ref T num, T val) where T : IComparable<T>
    { if (num.CompareTo(val) == -1) { num = val; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static void swap<T>(ref T v1, ref T v2)
    { var t = v2; v2 = v1; v1 = t; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static T[] Create<T>(int n, Func<T> f)
        => Enumerable.Repeat(0, n).Select(_ => f()).ToArray();
    public static void Fail() => Fail("No");
    public static void Fail<T>(T s) { WriteLine(s); Console.Out.Close(); Environment.Exit(0); }
    static void Main(string[] args)
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        var p = new Solver();
        for (var i = 1; i > 0; --i)
            p.Solve();
        Console.Out.Flush();
    }
}

public class Input
{
    public static string read => ReadLine().Trim();
    public static int[] ar => read.Split(' ').Select(int.Parse).ToArray();
    public static int num => ToInt32(read);
    public static long[] arL => read.Split(' ').Select(long.Parse).ToArray();
    public static long numL => ToInt64(read);
    public static char[][] grid(int h)
        => Create(h, () => read.ToCharArray());
    public static int[] ar1D(int n)
        => Create(n, () => num);
    public static long[] arL1D(int n)
        => Create(n, () => numL);
    public static string[] strs(int n)
        => Create(n, () => read);
    public static int[][] ar2D(int n)
        => Create(n, () => ar);
    public static long[][] arL2D(int n)
        => Create(n, () => arL);
    public static List<T>[] edge<T>(int n)
        => Create(n, () => new List<T>());
    public static void Make<T1, T2>(out T1 v1, out T2 v2)
    {
        v1 = Next<T1>();
        v2 = Next<T2>();
    }
    public static void Make<T1, T2, T3>(out T1 v1, out T2 v2, out T3 v3)
    {
        Make(out v1, out v2);
        v3 = Next<T3>();
    }
    public static void Make<T1, T2, T3, T4>(out T1 v1, out T2 v2, out T3 v3, out T4 v4)
    {
        Make(out v1, out v2, out v3);
        v4 = Next<T4>();
    }
    public static void Make<T1, T2, T3, T4, T5>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5)
    {
        Make(out v1, out v2, out v3, out v4);
        v5 = Next<T5>();
    }
    public static void Make<T1, T2, T3, T4, T5, T6>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6)
    {
        Make(out v1, out v2, out v3, out v4, out v5);
        v6 = Next<T6>();
    }
    static Input()
    {
        sc = new Queue<string>();
        dic = new Dictionary<Type, Func<string, object>>();
        dic[typeof(int)] = s => int.Parse(s);
        dic[typeof(long)] = s => long.Parse(s);
        dic[typeof(char)] = s => char.Parse(s);
        dic[typeof(double)] = s => double.Parse(s);
        dic[typeof(uint)] = s => uint.Parse(s);
        dic[typeof(ulong)] = s => ulong.Parse(s);
        dic[typeof(string)] = s => s;
    }
    private static Dictionary<Type, Func<string, object>> dic;
    private static Queue<string> sc;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static T Next<T>() { if (sc.Count == 0) foreach (var item in read.Split(' ')) sc.Enqueue(item); return (T)dic[typeof(T)](sc.Dequeue()); }
    public const int MOD = 1000000007;
}

public class Pair<T1, T2> : IComparable<Pair<T1, T2>>
{
    public T1 v1 { get; set; }
    public T2 v2 { get; set; }
    public Pair() { v1 = Input.Next<T1>(); v2 = Input.Next<T2>(); }
    public Pair(T1 v1, T2 v2)
    { this.v1 = v1; this.v2 = v2; }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public int CompareTo(Pair<T1, T2> p)
    {
        var c = Comparer<T1>.Default.Compare(v1, p.v1);
        if (c == 0)
            c = Comparer<T2>.Default.Compare(v2, p.v2);
        return c;
    }
    public override string ToString()
        => $"{v1.ToString()} {v2.ToString()}";
}

public class Pair<T1, T2, T3> : Pair<T1, T2>, IComparable<Pair<T1, T2, T3>>
{
    public T3 v3 { get; set; }
    public Pair() : base() { v3 = Input.Next<T3>(); }
    public Pair(T1 v1, T2 v2, T3 v3) : base(v1, v2)
    { this.v3 = v3; }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public int CompareTo(Pair<T1, T2, T3> p)
    {
        var c = base.CompareTo(p);
        if (c == 0)
            c = Comparer<T3>.Default.Compare(v3, p.v3);
        return c;
    }
    public override string ToString()
        => $"{base.ToString()} {v3.ToString()}";
}