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: Accepted)

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 Program
{
    static void Main(string[] args)
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
        var p = new Program();
        for (var i = 1; i > 0; --i)
            p.Solve();
        Console.Out.Flush();
    }
    void Solve()
    {
        int n, m, s, t;
        Input.Make(out n, out m, out s, out t);
        s--; t--;
        var inf = (long)1e15;
        var kedge = new WeightedGraph<long>(n);
        var yedge = new WeightedGraph<long>(n);
        for (var i = 0; i < m; i++)
        {
            int a, b, c, d;
            Input.Make(out a, out b, out c, out d);
            a--; b--;
            kedge.AddEdge(a, b, d);
            yedge.AddEdge(a, b, c);

        }
        var kdist = ShortestPath.RadixDijkstra(kedge, t);
        var ydist = ShortestPath.RadixDijkstra(yedge, s);
        var res = new List<long>();
        var min = long.MaxValue;
        for (var i = n - 1; i >= 0; i--)
        {
            chmin(ref min, kdist[i] + ydist[i]);
            res.Add(inf - min);
        }
        res.Reverse();

        WriteLine(string.Join("\n", res));
    }
}
namespace Graph
{
    #region テンプレート
    public class UnWeightedGraph
    {
        public List<int>[] edges { get; set; }
        public int Count { get; set; }
        public bool IsDirected { get; set; }
        public List<int> this[int index]
        { get { return edges[index]; } }
        public UnWeightedGraph(int length, bool isDirected = false)
        {
            edges = Enumerable.Repeat(0, length).Select(_ => new List<int>()).ToArray();
            Count = length;
            IsDirected = isDirected;
        }
        private UnWeightedGraph(List<int>[] edges)
        { this.edges = edges; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void AddEdge(int from,int to)
        {
            edges[from].Add(to);
            if (!IsDirected)
                edges[to].Add(from);
        }
        public static implicit operator UnWeightedGraph(List<int>[] edges)
            => new UnWeightedGraph(edges);
    }

    public class WeightedGraph<T> where T : IComparable<T>
    {
        public List<Edge<T>>[] edges { get; set; }
        public int Count { get; }
        public bool IsDirected { get; set; }
        public List<Edge<T>> this[int index]
        { get { return edges[index]; } }
        public WeightedGraph(int length, bool isDirected = false)
        {
            edges = Enumerable.Repeat(0, length).Select(_ => new List<Edge<T>>()).ToArray();
            Count = length;
            IsDirected = isDirected;
        }
        private WeightedGraph(List<Edge<T>>[] edges)
        { this.edges = edges; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void AddEdge(int from, int to, T cost)
        {
            edges[from].Add(new Edge<T>(to, cost));
            if (!IsDirected)
                edges[to].Add(new Edge<T>(from, cost));
        }
        public static implicit operator WeightedGraph<T>(List<Edge<T>>[] edges)
            => new WeightedGraph<T>(edges);
    }       
    //隣接行列で持つ
    public class DenceGraph<T> where T:IComparable<T>
    {
        public T[][] edges { get; set; }
        public int Count { get; }
        public T[] this[int index]
        { get { return edges[index]; } }
        public DenceGraph(int length)
        {
            edges = Enumerable.Repeat(0, length).Select(_ => new T[length]).ToArray();
            Count = length;
        }
    }

    public struct Edge<T> : IComparable<Edge<T>> where T : IComparable<T>
    {
        public int From { get; set; }
        public int To { get; set; }
        public T Cost { get; set; }
        public Edge(int to, T cost) : this(-1, to, cost) { }
        public Edge(int from, int to, T cost)
        { From = from; To = to; Cost = cost; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static implicit operator int(Edge<T> e)
            => e.To;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public int CompareTo(Edge<T> e)
            => Cost.CompareTo(e.Cost);
    }
    #endregion
}
namespace Graph
{
    using Number = System.Int64;        
    public class ShortestPath
    {
        #region ダイクストラ
        /// <summary>
        /// 負の重みの辺を持たないグラフでの単一始点最短距離をO(ElogV)で求める
        /// 依存:PriorityQueue,Pair
        /// </summary>
        /// <param name="edges"></param>
        /// <param name="st">始点</param>
        /// <returns></returns>
        public static Number[] Dijkstra(WeightedGraph<Number> edges, int st = 0)
        {
            var dist = Enumerable.Repeat(Number.MaxValue, edges.Count).ToArray();
            var pq = new PriorityQueue<Pair<Number, int>>(false);
            pq.Enqueue(new Pair<Number, int>(0, st));
            dist[st] = 0;
            while (pq.Count != 0)
            {
                var p = pq.Dequeue();
                if (dist[p.v2] < p.v1) continue;
                foreach (var e in edges[p.v2])
                    if (chmin(ref dist[e.To], e.Cost + p.v1))
                        pq.Enqueue(new Pair<Number, int>(dist[e.To], e.To));
            }
            return dist;
        }
        #endregion
        #region RadixHeapでのダイクストラ
        /// <summary>
        /// RadixHeapを用いて単一始点最短経路を求める
        /// 依存:RadixHeap
        /// </summary>
        /// <param name="edges"></param>
        /// <param name="st"></param>
        /// <returns></returns>
        public static Number[] RadixDijkstra(WeightedGraph<Number> edges,int st)
        {
            var dist = Enumerable.Repeat(Number.MaxValue, edges.Count).ToArray();
            var pq = new RadixHeap<int>();
            pq.Push(0, st);
            dist[st] = 0;
            while (pq.Count != 0)
            {
                var p = pq.Pop();
                if (dist[p.v2] < p.v1) continue;
                foreach (var e in edges[p.v2])
                    if (chmin(ref dist[e.To], e.Cost + p.v1))
                        pq.Push(dist[e.To], e.To);
            }
            return dist;
        }
        #endregion
        #region 密なグラフでのダイクストラ
        /// <summary>
        /// 負の重みの辺を持たないグラフでの単一始点最短経路をO(V^2)で求める
        /// </summary>
        /// <param name="gr"></param>
        /// <param name="st"></param>
        /// <returns></returns>
        public static Number[] Dijkstra(DenceGraph<Number> gr,int st)
        {
            var dist = Enumerable.Repeat(Number.MaxValue, gr.Count).ToArray();
            dist[st] = 0;
            var use = new bool[gr.Count];
            while (true)
            {
                var min = Number.MaxValue;
                var minj = -1;
                for (var i = 0; i < gr.Count; i++)
                    if (!use[i] && chmin(ref min, dist[i]))
                        minj = i;
                if (minj == -1) break;
                use[minj] = true;
                for (var i = 0; i < gr.Count; i++)
                    chmin(ref dist[i], dist[minj] + gr[minj][i]);
            }
            return dist;
        }
        #endregion
        #region ワーシャルフロイド
        /// <summary>
        /// 全点対最短距離をO(V^3)で求める
        /// </summary>
        /// <param name="num">頂点数</param>
        /// <param name="edges">辺の集合</param>
        /// <param name="directed">有向グラフか</param>
        /// <returns></returns>
        public static Number[][] WarshallFloyd(int num, IEnumerable<Edge<Number>> edges, bool directed = false)
        {
            var dist = Enumerable.Repeat(0, num).Select(_ => Enumerable.Repeat(Number.MaxValue / 2, num).ToArray()).ToArray();
            foreach (var e in edges)
            {
                dist[e.From][e.To] = e.Cost;
                if (!directed)
                    dist[e.To][e.From] = e.Cost;
            }
            for (var k = 0; k < num; k++)
                for (var i = 0; i < num; i++)
                    for (var j = 0; j < num; j++)
                        chmin(ref dist[i][j], dist[i][k] + dist[k][j]);
            return dist;
        }
        #endregion
        #region ベルマンフォード
        /// <summary>
        /// 有向グラフ上の単一始点最短距離をO(VE)で求める
        /// </summary>
        /// <param name="num">頂点数</param>
        /// <param name="edges">辺の集合</param>
        /// <param name="st">始点</param>
        /// <param name="dist">始点からの最短距離</param>
        /// <returns>始点から辿り着ける負閉路が存在した場合、false</returns>
        static bool BellmanFord(int num, IEnumerable<Edge<Number>> edges, int st, out long[] dist)
        {
            dist = Enumerable.Repeat(long.MaxValue, num).ToArray();
            dist[st] = 0;
            for (var i = 0; i < num - 1; i++)
                foreach (var e in edges)
                    if (dist[e.From] != long.MaxValue)
                        chmin(ref dist[e.To], dist[e.From] + e.Cost);
            for (var i = 0; i < num; i++)
                foreach (var e in edges)
                {
                    if (dist[e.From] == long.MaxValue) continue;
                    if (dist[e.To] > dist[e.From] + e.Cost)
                        return false;
                }
            return true;
        }
        #endregion
    }
}
namespace DataStructure
{
    using C = System.Int64;
    public class RadixHeap<T>
    {
        public int Count { get; set; }
        private C last;
        private List<Pair<C, T>>[] v;
        private int len;
        public RadixHeap()
        {
            len = Convert.ToString(C.MaxValue, 2).Length;
            v = Enumerable.Repeat(0, len + 2).Select(_ => new List<Pair<C, T>>()).ToArray();
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        private int GetBit(C a)
        {
            for (var i = len; i >= 0; i--)
                if ((1 & a >> i) == 1)
                    return i + 1;
            return 0;
        }
        public void Push(Pair<C, T> p)
            => Push(p.v1, p.v2);
        /// <summary>
        /// last(=最後にpopしたもののkey)以上のkeyについて(key,value)をpushします
        /// </summary>
        /// <param name="key"></param>
        /// <param name="value"></param>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Push(C key, T value)
        {
            Count++;
            v[GetBit(key ^ last)].Add(new Pair<C, T>(key, value));
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public Pair<C, T> Pop()
        {
            if (v[0].Count == 0)
            {
                var ind = 1;
                while (v[ind].Count == 0) ind++;
                last = v[ind].Min().v1;
                foreach (var p in v[ind])
                    v[GetBit(p.v1 ^ last)].Add(p);
                v[ind].Clear();
            }
            Count--;
            var ret = v[0].Last();
            v[0].RemoveAt(v[0].Count - 1);
            return ret;
        }
    }
}
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();
        }
    }
    private int Compare(int i, int j) => (IsMaxHeap ? 1 : -1) * _item[i].CompareTo(_item[j]);
    private void Swap(int i, int j) { var t = _item[i]; _item[i] = _item[j]; _item[j] = t; }
    private int Parent(int i)
        => (i - 1) >> 1;
    private int Left(int i)
        => (i << 1) + 1;
    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;
    }
    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);
        }
    }
    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; }
    public static void Fail() => Fail("No");
    public static void Fail<T>(T s) { WriteLine(s); Console.Out.Close(); Environment.Exit(0); }
}
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);
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static T[] Create<T>(int n, Func<T> f)
        => Enumerable.Repeat(0, n).Select(_ => f()).ToArray();
    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 override bool Equals(object obj)
        => this == (Pair<T1, T2>)obj;
    public override int GetHashCode()
        => v1.GetHashCode() ^ v2.GetHashCode();
    public static bool operator ==(Pair<T1, T2> p1, Pair<T1, T2> p2)
        => p1.CompareTo(p2) == 0;
    public static bool operator !=(Pair<T1, T2> p1, Pair<T1, T2> p2)
        => p1.CompareTo(p2) != 0;
    public static bool operator >(Pair<T1, T2> p1, Pair<T1, T2> p2)
        => p1.CompareTo(p2) == 1;
    public static bool operator >=(Pair<T1, T2> p1, Pair<T1, T2> p2)
        => p1.CompareTo(p2) != -1;
    public static bool operator <(Pair<T1, T2> p1, Pair<T1, T2> p2)
        => p1.CompareTo(p2) == -1;
    public static bool operator <=(Pair<T1, T2> p1, Pair<T1, T2> p2)
        => p1.CompareTo(p2) != 1;
}

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()}";
}