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.Linq;
using System.Collections.Generic;

namespace Contest
{
    class Program
    {
        static void Main(string[] args)
        {
            SoundHound.D();
        }

        class SoundHound
        {
            public static void D()
            {
                var N = Read.Int();
                var M = Read.Int();
                var S = Read.Int();
                var T = Read.Int();
                List<Tuple<int, int, long>> Edges_A = new List<Tuple<int, int, long>>();
                List<Tuple<int, int, long>> Edges_B = new List<Tuple<int, int, long>>();
                for(int i = 0; i < M; ++i)
                {
                    var u = Read.Int();
                    var v = Read.Int();
                    var a = Read.Long();
                    var b = Read.Long();
                    Edges_A.Add(new Tuple<int, int, long>(u, v, a));
                    Edges_A.Add(new Tuple<int, int, long>(v, u, a));
                    Edges_B.Add(new Tuple<int, int, long>(u, v, b));
                    Edges_B.Add(new Tuple<int, int, long>(v, u, b));
                }
                var Adj_A = Util.GenAdjacencyList(N, Edges_A.ToArray());
                var Adj_B = Util.GenAdjacencyList(N, Edges_B.ToArray());
                var distA = Util.Dijkstra(Adj_A, N, M, S);
                var distB = Util.Dijkstra(Adj_B, N, M, T);
                long[] max = new long[N];
                long Init = 1000000000000000;
                max[N - 1] = Init - distA[N] - distB[N];
                for(int n = N - 2; n >= 0; --n)
                {
                    var cost = Init - distA[n + 1] - distB[n + 1];
                    max[n] = Math.Max(max[n + 1], cost);
                }
                for(int i = 0; i < N; ++i)
                {
                    Console.WriteLine(max[i]);
                }
            }
        }

        class Util
        {
            public class PriorityQueue<T> where T : IComparable
            {
                private IComparer<T> _comparer = null;
                private bool _isAsc = true;

                private T[] _heap;
                private int _sz = 0;

                public PriorityQueue(int maxSize, IComparer<T> comparer)
                {
                    _heap = new T[maxSize];
                    _comparer = comparer;
                }
                public PriorityQueue(int maxSize, bool isAsc = true)
                {
                    _heap = new T[maxSize];
                    _isAsc = isAsc;
                }

                private int Compare(T x, T y)
                {
                    if (_comparer != null) return _comparer.Compare(x, y);
                    return _isAsc ? x.CompareTo(y) : y.CompareTo(x);
                }

                public void Push(T x)
                {
                    //node number
                    var i = _sz++;

                    while (i > 0)
                    {
                        //parent node number
                        var p = (i - 1) / 2;

                        if (Compare(_heap[p], x) <= 0) break;

                        _heap[i] = _heap[p];
                        i = p;
                    }

                    _heap[i] = x;
                }

                public T Pop()
                {
                    T ret = _heap[0];
                    T x = _heap[--_sz];

                    int i = 0;
                    while (i * 2 + 1 < _sz)
                    {
                        //children
                        int a = i * 2 + 1;
                        int b = i * 2 + 2;

                        if (b < _sz && Compare(_heap[b], _heap[a]) < 0) a = b;

                        if (Compare(_heap[a], x) >= 0) break;

                        _heap[i] = _heap[a];
                        i = a;
                    }

                    _heap[i] = x;

                    return ret;
                }
                public int Count() { return _sz; }
                public T Peek() { return _heap[0]; }
                public bool Contains(T x) { for (int i = 0; i < _sz; i++) if (x.Equals(_heap[i])) return true; return false; }
            }
            public class MyTuple<T1,T2> : IComparable where T1: IComparable<T1>
            {
                public readonly T1 Item1; public readonly T2 Item2;
                public MyTuple(T1 item1,T2 item2) { Item1 = item1;Item2 = item2; }
                public int CompareTo(object obj) { return Item1.CompareTo(((MyTuple<T1, T2>)obj).Item1); }
            }
            public static long[] Dijkstra(Dictionary<int, Dictionary<int, long>> adj, int N, int M, int start)
            {
                long INF = 1000000000000;
                var dist = Enumerable.Range(0, N + 1).Select(i => INF).ToArray();
                var queue = new PriorityQueue<MyTuple<long, int>>(N + M + 100);
                dist[start] = 0;
                queue.Push(new MyTuple<long, int>(0, start));
                while (queue.Count() > 0)
                {
                    var kvp = queue.Pop();
                    var d = kvp.Item1; var v = kvp.Item2;
                    if(dist[v] < d) { continue; }
                    dist[v] = d;
                    foreach(var kvp2 in adj[v])
                    {
                        var newV = kvp2.Key;
                        var newD = dist[v] + kvp2.Value;
                        if (newD < dist[newV])
                        {
                            dist[newV] = newD;
                            queue.Push(new MyTuple<long, int>(newD, newV));
                        }
                    }
                }
                return dist;
            }
            public static Dictionary<int, Dictionary<int, long>> GenAdjacencyList(int N, Tuple<int, int, long>[] edges)
            {
                Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>();
                for (int i = 0; i <= N; ++i)
                {
                    dict.Add(i, new Dictionary<int, long>());
                }
                foreach (var edge in edges)
                {
                    dict[edge.Item1].Add(edge.Item2, edge.Item3);
                }
                return dict;
            }
        }

        class Graph
        {
        }

        static class Read
        {
            static Queue<string> queue = new Queue<string>();
            static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
            public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
            public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
            public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
            public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
            public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
            public static string[] StrN() { return Console.ReadLine().Split(' '); }
            public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
            public static long[,] LongMatrix(int r, int c)
            {
                var mat = new long[r, c];
                for (int i = 0; i < r; ++i)
                {
                    var x = Read.LongN();
                    for (int j = 0; j < c; ++j)
                    {
                        mat[i, j] = x[j];
                    }
                }
                return mat;
            }
            public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M)
            {
                Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
                for (int i = 0; i <= N; ++i)
                {
                    dict.Add(i, new HashSet<int>());
                }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN();
                    dict[ab[0]].Add(ab[1]);
                    dict[ab[1]].Add(ab[0]);
                }
                return dict;
            }
            public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M)
            {
                Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>();
                for (int i = 0; i <= N; ++i)
                {
                    dict.Add(i, new Dictionary<int, long>());
                }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN();
                    dict[ab[0]].Add(ab[1], ab[2]);
                    dict[ab[1]].Add(ab[0], ab[2]);
                }
                return dict;
            }
        }
    }
}