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.IO;
using System.Linq;
using static System.Math;
using System.Text;
using System.Threading;
using System.Globalization;
using System.Runtime.CompilerServices;
using Library;

namespace Program
{
    public static class SOUNDHOUND2018_SUMMER_QUALD
    {
        static public int numberOfRandomCases = 0;
        static public void MakeTestCase(List<string> _input, List<string> _output, ref Func<string[], bool> _outputChecker)
        {
        }
        static public void Solve()
        {
            var n = NN;
            var m = NN;
            var s = NN - 1;
            var t = NN - 1;
            var uvab = Repeat(0, m).Select(_ => new { u = (int)NN - 1, v = (int)NN - 1, a = NN, b = NN }).ToArray();
            var enPath = Repeat(0, n).Select(_ => new Dictionary<int, long>()).ToArray();
            var sunukuPath = Repeat(0, n).Select(_ => new Dictionary<int, long>()).ToArray();
            foreach (var item in uvab)
            {
                enPath[item.u][item.v] = item.a;
                sunukuPath[item.u][item.v] = item.b;
                enPath[item.v][item.u] = item.a;
                sunukuPath[item.v][item.u] = item.b;
            }
            var nodeNum = n;
            var enDist = Repeat(long.MaxValue >> 2, nodeNum).ToArray();
            {
                var start = s;
                var pred = new int?[nodeNum];
                enDist[start] = 0;
                var q = new LIB_PriorityQueue<long, int>();
                q.Push(0, (int)start);
                while (q.Count > 0)
                {
                    var u = q.Pop().Value;
                    foreach (var pathItem in enPath[u])
                    {
                        var v = pathItem.Key;
                        var alt = enDist[u] + pathItem.Value;
                        if (enDist[v] > alt)
                        {
                            enDist[v] = alt;
                            pred[v] = u;
                            q.Push(alt, v);
                        }
                    }
                }
            }
            var sunukuDist = Repeat(long.MaxValue >> 2, nodeNum).ToArray();
            {
                var start = t;
                var pred = new int?[nodeNum];
                sunukuDist[start] = 0;
                var q = new LIB_PriorityQueue<long, int>();
                q.Push(0, (int)start);
                while (q.Count > 0)
                {
                    var u = q.Pop().Value;
                    foreach (var pathItem in sunukuPath[u])
                    {
                        var v = pathItem.Key;
                        var alt = sunukuDist[u] + pathItem.Value;
                        if (sunukuDist[v] > alt)
                        {
                            sunukuDist[v] = alt;
                            pred[v] = u;
                            q.Push(alt, v);
                        }
                    }
                }
            }
            var ans = new long[n];
            var min = 10000000000000000;
            for (var i = n - 1; i >= 0; i--)
            {
                var sumEnSunuku = enDist[i] + sunukuDist[i];
                min = Min(min, sumEnSunuku);
                ans[i] = min;
            }
            for (var i = 0; i < n; i++)
            {
                Console.WriteLine(1000000000000000 - ans[i]);
            }
        }
        static class Console_
        {
            static Queue<string> param = new Queue<string>();
            public static string NextString() { if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item); return param.Dequeue(); }
        }
        class Printer : StreamWriter
        {
            public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
            public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { base.AutoFlush = false; }
            public Printer(Stream stream, Encoding encoding) : base(stream, encoding) { base.AutoFlush = false; }
        }
        static public void Main(string[] args) { if (args.Length == 0) { Console.SetOut(new Printer(Console.OpenStandardOutput())); } var t = new Thread(Solve, 134217728); t.Start(); t.Join(); Console.Out.Flush(); }
        static long NN => long.Parse(Console_.NextString());
        static double ND => double.Parse(Console_.NextString());
        static string NS => Console_.NextString();
        static long[] NNList(long N) => Repeat(0, N).Select(_ => NN).ToArray();
        static double[] NDList(long N) => Repeat(0, N).Select(_ => ND).ToArray();
        static string[] NSList(long N) => Repeat(0, N).Select(_ => NS).ToArray();
        static IEnumerable<T> OrderByRand<T>(this IEnumerable<T> x) => x.OrderBy(_ => xorshift);
        static long Count<T>(this IEnumerable<T> x, Func<T, bool> pred) => Enumerable.Count(x, pred);
        static IEnumerable<T> Repeat<T>(T v, long n) => Enumerable.Repeat<T>(v, (int)n);
        static IEnumerable<int> Range(long s, long c) => Enumerable.Range((int)s, (int)c);
        static uint xorshift { get { _xsi.MoveNext(); return _xsi.Current; } }
        static IEnumerator<uint> _xsi = _xsc();
        static IEnumerator<uint> _xsc() { uint x = 123456789, y = 362436069, z = 521288629, w = (uint)(DateTime.Now.Ticks & 0xffffffff); while (true) { var t = x ^ (x << 11); x = y; y = z; z = w; w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)); yield return w; } }
    }
}
namespace Library {
    class LIB_PriorityQueue<T>
    {
        List<T> heap;
        Comparison<T> comp;
        public T Peek => heap[0];
        public int Count => heap.Count;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_PriorityQueue(int cap, Comparison<T> cmp, bool asc = true)
        {
            heap = new List<T>(cap);
            comp = asc ? cmp : (x, y) => cmp(y, x);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_PriorityQueue(Comparison<T> cmp, bool asc = true)
        {
            heap = new List<T>();
            comp = asc ? cmp : (x, y) => cmp(y, x);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_PriorityQueue(int cap, bool asc = true) : this(cap, Comparer<T>.Default.Compare, asc) { }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_PriorityQueue(bool asc = true) : this(Comparer<T>.Default.Compare, asc) { }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Push(T val)
        {
            var i = heap.Count;
            heap.Add(val);
            while (i > 0)
            {
                var ni = (i - 1) / 2;
                if (comp(val, heap[ni]) >= 0) break;
                heap[i] = heap[ni];
                i = ni;
            }
            heap[i] = val;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public T Pop()
        {
            var ret = heap[0];
            var val = heap[heap.Count - 1];
            heap.RemoveAt(heap.Count - 1);
            if (heap.Count == 0) return ret;
            var i = 0; while ((i << 1) + 1 < heap.Count)
            {
                var i1 = (i << 1) + 1;
                var i2 = (i << 1) + 2;
                if (i2 < heap.Count && comp(heap[i1], heap[i2]) > 0) i1 = i2;
                if (comp(val, heap[i1]) <= 0) break;
                heap[i] = heap[i1]; i = i1;
            }
            heap[i] = val;
            return ret;
        }
    }
    class LIB_PriorityQueue<TK, TV>
    {
        LIB_PriorityQueue<KeyValuePair<TK, TV>> q;
        public KeyValuePair<TK, TV> Peek => q.Peek;
        public int Count => q.Count;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_PriorityQueue(int cap, Comparison<TK> cmp, bool asc = true)
        {
            q = new LIB_PriorityQueue<KeyValuePair<TK, TV>>(cap, (x, y) => cmp(x.Key, y.Key), asc);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_PriorityQueue(Comparison<TK> cmp, bool asc = true)
        {
            q = new LIB_PriorityQueue<KeyValuePair<TK, TV>>((x, y) => cmp(x.Key, y.Key), asc);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_PriorityQueue(int cap, bool asc = true) : this(cap, Comparer<TK>.Default.Compare, asc) { }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_PriorityQueue(bool asc = true) : this(Comparer<TK>.Default.Compare, asc) { }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void Push(TK k, TV v) => q.Push(new KeyValuePair<TK, TV>(k, v));
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public KeyValuePair<TK, TV> Pop() => q.Pop();
    }
}